In this note, a diffusive predator-prey model subject to the homogeneous Neumann bound- ary condition is investigated and some qualitative analysis of solutions to this reaction-diffusion system and its corresponding ...In this note, a diffusive predator-prey model subject to the homogeneous Neumann bound- ary condition is investigated and some qualitative analysis of solutions to this reaction-diffusion system and its corresponding steady-state problem is presented. In particular, by use of a Lyapunov function, the global stability of the constant positive steady state is discussed. For the associated steady state problem, a priori estimates for positive steady states are derived and some non-existence results for non-constant positive steady states are also established when one of the diffusion rates is large enough. Consequently, our results extend and complement the existing ones on this model.展开更多
Subject to the homogeneous Neumann boundary condition, a ratio-dependent predator-prey reaction diffusion model is discussed. An improved result for the model is derived, that is, the unique positive constant steady s...Subject to the homogeneous Neumann boundary condition, a ratio-dependent predator-prey reaction diffusion model is discussed. An improved result for the model is derived, that is, the unique positive constant steady state is the global stability. This is done using the comparison principle and establishing iteration schemes involving positive solutions supremum and infimum. The result indicates that the two species will ultimately distribute homogeneously in space. In fact, the comparison argument and iteration technique to be used in this paper can be applied to some other models. This method deals with the not-existence of a non-constant positive steady state for some reaction diffusion systems, which is rather simple but sufficiently effective.展开更多
Scalable simulation leveraging real-world data plays an essential role in advancing autonomous driving,owing to its efficiency and applicability in both training and evaluating algorithms.Consequently,there has been i...Scalable simulation leveraging real-world data plays an essential role in advancing autonomous driving,owing to its efficiency and applicability in both training and evaluating algorithms.Consequently,there has been increasing attention on generating highly realistic and consistent driving videos,particularly those involving viewpoint changes guided by the control commands or trajectories of ego vehicles.However,current reconstruction approaches,such as Neural Radiance Fields and 3D Gaussian Splatting,frequently suffer from limited generalization and depend on substantial input data.Meanwhile,2D generative models,though capable of producing unknown scenes,still have room for improvement in terms of coherence and visual realism.To overcome these challenges,we introduce GenScene,a world model that synthesizes front-view driving videos conditioned on trajectories.A new temporal module is presented to improve video consistency by extracting the global context of each frame,calculating relationships of frames using these global representations,and fusing frame contexts accordingly.Moreover,we propose an innovative attention mechanism that computes relations of pixels within each frame and pixels in the corresponding window range of the initial frame.Extensive experiments show that our approach surpasses various state-of-the-art models in driving video generation,and the introduced modules contribute significantly to model performance.This work establishes a new paradigm for goal-oriented video synthesis in autonomous driving,which facilitates on-demand simulation to expedite algorithm development.展开更多
In this paper,we are concerned with the stability of traveling wavefronts of a Belousov-Zhabotinsky model with mixed nonlocal and degenerate diffusions.Such a system can be used to study the competition among nonlocal...In this paper,we are concerned with the stability of traveling wavefronts of a Belousov-Zhabotinsky model with mixed nonlocal and degenerate diffusions.Such a system can be used to study the competition among nonlocally diffusive species and degenerately diffusive species.We prove that the traveling wavefronts are exponentially stable,when the initial perturbation around the traveling waves decays exponentially as x→-∞,but in other locations,the initial data can be arbitrarily large.The adopted methods are the weighted energy with the comparison principle and squeezing technique.展开更多
In this paper,we propose a new privacy-aware transmission scheduling algorithm for 6G ad hoc networks.This system enables end nodes to select the optimum time and scheme to transmit private data safely.In 6G dynamic h...In this paper,we propose a new privacy-aware transmission scheduling algorithm for 6G ad hoc networks.This system enables end nodes to select the optimum time and scheme to transmit private data safely.In 6G dynamic heterogeneous infrastructures,unstable links and non-uniform hardware capabilities create critical issues regarding security and privacy.Traditional protocols are often too computationally heavy to allow 6G services to achieve their expected Quality-of-Service(QoS).As the transport network is built of ad hoc nodes,there is no guarantee about their trustworthiness or behavior,and transversal functionalities are delegated to the extreme nodes.However,while security can be guaranteed in extreme-to-extreme solutions,privacy cannot,as all intermediate nodes still have to handle the data packets they are transporting.Besides,traditional schemes for private anonymous ad hoc communications are vulnerable against modern intelligent attacks based on learning models.The proposed scheme fulfills this gap.Findings show the probability of a successful intelligent attack reduces by up to 65%compared to ad hoc networks with no privacy protection strategy when used the proposed technology.While congestion probability can remain below 0.001%,as required in 6G services.展开更多
Human motion modeling is a core technology in computer animation,game development,and humancomputer interaction.In particular,generating natural and coherent in-between motion using only the initial and terminal frame...Human motion modeling is a core technology in computer animation,game development,and humancomputer interaction.In particular,generating natural and coherent in-between motion using only the initial and terminal frames remains a fundamental yet unresolved challenge.Existing methods typically rely on dense keyframe inputs or complex prior structures,making it difficult to balance motion quality and plausibility under conditions such as sparse constraints,long-term dependencies,and diverse motion styles.To address this,we propose a motion generation framework based on a frequency-domain diffusion model,which aims to better model complex motion distributions and enhance generation stability under sparse conditions.Our method maps motion sequences to the frequency domain via the Discrete Cosine Transform(DCT),enabling more effective modeling of low-frequency motion structures while suppressing high-frequency noise.A denoising network based on self-attention is introduced to capture long-range temporal dependencies and improve global structural awareness.Additionally,a multi-objective loss function is employed to jointly optimize motion smoothness,pose diversity,and anatomical consistency,enhancing the realism and physical plausibility of the generated sequences.Comparative experiments on the Human3.6M and LaFAN1 datasets demonstrate that our method outperforms state-of-the-art approaches across multiple performance metrics,showing stronger capabilities in generating intermediate motion frames.This research offers a new perspective and methodology for human motion generation and holds promise for applications in character animation,game development,and virtual interaction.展开更多
This article is concerned with the existence of traveling wave solutions for a discrete diffusive ratio-dependent predator-prey model. By applying Schauder’s fixed point theorem with the help of suitable upper and lo...This article is concerned with the existence of traveling wave solutions for a discrete diffusive ratio-dependent predator-prey model. By applying Schauder’s fixed point theorem with the help of suitable upper and lower solutions, we prove that there exists a positive constant c* such that when c > c* , the discrete diffusive predator-prey system admits an invasion traveling wave. The existence of an invasion traveling wave with c = c* is also established by a limiting argument and a delicate analysis of the boundary conditions.Finally, by the asymptotic spreading theory and the comparison principle, the non-existence of invasion traveling waves with speed c < c* is also proved.展开更多
In this paper,we consider a diffusive Holling-Tanner predator prey model with Smith growth subject to Neumann boundary condition.We analyze the local stability,exis-tence of a Hopf bifurcation at the co-existence of t...In this paper,we consider a diffusive Holling-Tanner predator prey model with Smith growth subject to Neumann boundary condition.We analyze the local stability,exis-tence of a Hopf bifurcation at the co-existence of the equilibrium and stability of bifur-cating periodic solutions of the system in the absence of diffusion.Furthermore the Turing instability and Hopf bifurcation analysis of the system with diffusion are studied.Finally numerical simulations are given to demonstrate the effectiveness of the theoretical analysis.展开更多
The dynamical behaviors of a diffusive predator-prey model with Beddington-DeAngelis functional response and disease in the prey is considered in this work. By applying the comparison principle, linearized method, Lya...The dynamical behaviors of a diffusive predator-prey model with Beddington-DeAngelis functional response and disease in the prey is considered in this work. By applying the comparison principle, linearized method, Lyapunov function and iterative method, we are able to achieve sufficient conditions of the permanence, the local stability and global stability of the boundary equilibria and the positive equilibrium, respectively. Our result complements and supplements some known ones.展开更多
We study local dynamics of a diffusive predator-prey model in a spatially heterogeneous environment,where intrinsic growth rate of the prey is spatially ho-mogeneous,whereas carrying capacity of the habitat is spatial...We study local dynamics of a diffusive predator-prey model in a spatially heterogeneous environment,where intrinsic growth rate of the prey is spatially ho-mogeneous,whereas carrying capacity of the habitat is spatially inhomogeneous.In comparison with the existing predator-prey models,the stability of semi-trivial steady state of this model displays distinct properties.For example,for certain intermediate ranges of the death rate of the predator,the semi-trivial steady state can change its stability at least once as the dispersal rate of the prey varies from small to large,while the stability of the semi-trivial steady state is immune from the dispersal rate of the predator.展开更多
In this paper,we study a diffusive predator-prey model with hyperbolic mortality and prey-taxis under homogeneous Neumann boundary condition.We first analyze the influence of prey-taxis on the local stability of const...In this paper,we study a diffusive predator-prey model with hyperbolic mortality and prey-taxis under homogeneous Neumann boundary condition.We first analyze the influence of prey-taxis on the local stability of constant equilibria.It turns out that prey-taxis has influence on the stability of the unique positive constant equilibrium,but has no influence on the stability of the trivial equilibrium and the semi-trivial equilibrium.We then derive Hopf bifurcation and steady state bifurcation related to prey-taxis,which imply that the prey-taxis plays an important role in the dynamics.展开更多
The purpose of this paper is to study the traveling wave solutions of a diffusive predator- prey model with predator saturation and competition functional response. The system admits three equilibria： a zero equilibr...The purpose of this paper is to study the traveling wave solutions of a diffusive predator- prey model with predator saturation and competition functional response. The system admits three equilibria： a zero equilibrium E0, a boundary equilibrium E1 and a posi- tive equilibrium E. under some conditions. We establish the existence of two types of traveling wave solutions which connect E0 and E. and E1 and E., respectively. Our main arguments are based on a simplified shooting method, a sandwich method and constructions of appropriate Lyapunov functions. Our particular interest is to investi- gate the oscillation of both types of traveling wave solutions when they approach the positive equilibrium.展开更多
In this paper, spatial patterns of a diffusive predator-prey model with sigmoid （Holling type III） ratio-dependent functional response which concerns the influence of logistic population growth in prey and intra-spe...In this paper, spatial patterns of a diffusive predator-prey model with sigmoid （Holling type III） ratio-dependent functional response which concerns the influence of logistic population growth in prey and intra-species competition among predators are investigated. The （local and global） asymptotic stability behavior of the corresponding non- spatial model around the unique positive interior equilibrium point in homogeneous steady state is obtained. In addition, we derive the conditions for Turing instability and the consequent parametric Turing space in spatial domain. The results of spatial pat- tern analysis through numerical simulations are depicted and analyzed. ~rthermore, we perform a series of numerical simulations and find that the proposed model dynamics exhibits complex pattern replication. The feasible results obtained in this paper indicate that the effect of diffusion in Turing instability plays an important role to understand better the pattern formation in ecosystem.展开更多
This article is focusing on a class of multi-delay predator-prey model with feedback controls and prey diffusion. By developing some new analysis methods and using the theory of differential inequalities as well as co...This article is focusing on a class of multi-delay predator-prey model with feedback controls and prey diffusion. By developing some new analysis methods and using the theory of differential inequalities as well as constructing a suitable Lyapunov function, we establish a set of easily verifiable sufficient conditions which guarantee the permanence of the system and the globally attractivity of positive solution for the predator-prey system.Furthermore, some conditions for the existence, uniqueness and stability of positive periodic solution for the corresponding periodic system are obtained by using the fixed point theory and some new analysis techniques. In additional, some numerical solutions of the equations describing the system are given to verify the obtained criteria are new, general, and easily verifiable. Finally, we still solve numerically the corresponding stochastic predator-prey models with multiplicative noise sources, and obtain some new interesting dynamical behaviors of the system.展开更多
Accurately identifying building distribution from remote sensing images with complex background information is challenging.The emergence of diffusion models has prompted the innovative idea of employing the reverse de...Accurately identifying building distribution from remote sensing images with complex background information is challenging.The emergence of diffusion models has prompted the innovative idea of employing the reverse denoising process to distill building distribution from these complex backgrounds.Building on this concept,we propose a novel framework,building extraction diffusion model(BEDiff),which meticulously refines the extraction of building footprints from remote sensing images in a stepwise fashion.Our approach begins with the design of booster guidance,a mechanism that extracts structural and semantic features from remote sensing images to serve as priors,thereby providing targeted guidance for the diffusion process.Additionally,we introduce a cross-feature fusion module(CFM)that bridges the semantic gap between different types of features,facilitating the integration of the attributes extracted by booster guidance into the diffusion process more effectively.Our proposed BEDiff marks the first application of diffusion models to the task of building extraction.Empirical evidence from extensive experiments on the Beijing building dataset demonstrates the superior performance of BEDiff,affirming its effectiveness and potential for enhancing the accuracy of building extraction in complex urban landscapes.展开更多
In this paper, a three species diffusive predator-prey model with functional response is studied, where all parameters are time dependent. By using the continuation theorem of coincidence degree theory, the existence ...In this paper, a three species diffusive predator-prey model with functional response is studied, where all parameters are time dependent. By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for this system is established.展开更多
Imputation of missing data has long been an important topic and an essential application for intelligent transportation systems(ITS)in the real world.As a state-of-the-art generative model,the diffusion model has prov...Imputation of missing data has long been an important topic and an essential application for intelligent transportation systems(ITS)in the real world.As a state-of-the-art generative model,the diffusion model has proven highly successful in image generation,speech generation,time series modelling etc.and now opens a new avenue for traffic data imputation.In this paper,we propose a conditional diffusion model,called the implicit-explicit diffusion model,for traffic data imputation.This model exploits both the implicit and explicit feature of the data simultaneously.More specifically,we design two types of feature extraction modules,one to capture the implicit dependencies hidden in the raw data at multiple time scales and the other to obtain the long-term temporal dependencies of the time series.This approach not only inherits the advantages of the diffusion model for estimating missing data,but also takes into account the multiscale correlation inherent in traffic data.To illustrate the performance of the model,extensive experiments are conducted on three real-world time series datasets using different missing rates.The experimental results demonstrate that the model improves imputation accuracy and generalization capability.展开更多
Air target intent recognition holds significant importance in aiding commanders to assess battlefield situations and secure a competitive edge in decision-making.Progress in this domain has been hindered by challenges...Air target intent recognition holds significant importance in aiding commanders to assess battlefield situations and secure a competitive edge in decision-making.Progress in this domain has been hindered by challenges posed by imbalanced battlefield data and the limited robustness of traditional recognition models.Inspired by the success of diffusion models in addressing visual domain sample imbalances,this paper introduces a new approach that utilizes the Markov Transfer Field(MTF)method for time series data visualization.This visualization,when combined with the Denoising Diffusion Probabilistic Model(DDPM),effectively enhances sample data and mitigates noise within the original dataset.Additionally,a transformer-based model tailored for time series visualization and air target intent recognition is developed.Comprehensive experimental results,encompassing comparative,ablation,and denoising validations,reveal that the proposed method achieves a notable 98.86%accuracy in air target intent recognition while demonstrating exceptional robustness and generalization capabilities.This approach represents a promising avenue for advancing air target intent recognition.展开更多
The application of generative artificial intelligence(AI)is bringing about notable changes in anime creation.This paper surveys recent advancements and applications of diffusion and language models in anime generation...The application of generative artificial intelligence(AI)is bringing about notable changes in anime creation.This paper surveys recent advancements and applications of diffusion and language models in anime generation,focusing on their demonstrated potential to enhance production efficiency through automation and personalization.Despite these benefits,it is crucial to acknowledge the substantial initial computational investments required for training and deploying these models.We conduct an in-depth survey of cutting-edge generative AI technologies,encompassing models such as Stable Diffusion and GPT,and appraise pivotal large-scale datasets alongside quantifiable evaluation metrics.Review of the surveyed literature indicates the achievement of considerable maturity in the capacity of AI models to synthesize high-quality,aesthetically compelling anime visual images from textual prompts,alongside discernible progress in the generation of coherent narratives.However,achieving perfect long-form consistency,mitigating artifacts like flickering in video sequences,and enabling fine-grained artistic control remain critical ongoing challenges.Building upon these advancements,research efforts have increasingly pivoted towards the synthesis of higher-dimensional content,such as video and three-dimensional assets,with recent studies demonstrating significant progress in this burgeoning field.Nevertheless,formidable challenges endure amidst these advancements.Foremost among these are the substantial computational exigencies requisite for training and deploying these sophisticated models,particularly pronounced in the realm of high-dimensional generation such as video synthesis.Additional persistent hurdles include maintaining spatial-temporal consistency across complex scenes and mitigating ethical considerations surrounding bias and the preservation of human creative autonomy.This research underscores the transformative potential and inherent complexities of AI-driven synergy within the creative industries.We posit that future research should be dedicated to the synergistic fusion of diffusion and autoregressive models,the integration of multimodal inputs,and the balanced consideration of ethical implications,particularly regarding bias and the preservation of human creative autonomy,thereby establishing a robust foundation for the advancement of anime creation and the broader landscape of AI-driven content generation.展开更多
This paper examines an epidemic predator-prey model with prey dispersal and Holling type-II functional response. In this model, it is assumed that the predator population suffers a transmissible disease. By analyzing ...This paper examines an epidemic predator-prey model with prey dispersal and Holling type-II functional response. In this model, it is assumed that the predator population suffers a transmissible disease. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the coexistence equilibrium is addressed. Using Lyapunov functionals and LaSalle's invariance principle, we obtained the sufficient conditions for the global stability of the trivial equilibrium, the predator-extinction equilibrium, the disease-free equilibrium and the coexistence equilibrium, respectively. The paper also includes numerical simulations to illustrate the analytical results.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 10801090, 10871185, 10726016)supported by the Scientifio Research Projects of Hubei Provincial Department of Education (Grant No. Q200713001)+1 种基金Scientific Innovation Team Project of Hubei Provincial Department of Education (Grant No. T200809)supported by National Natural Science Foundation of China (Grant No. 10771032)
文摘In this note, a diffusive predator-prey model subject to the homogeneous Neumann bound- ary condition is investigated and some qualitative analysis of solutions to this reaction-diffusion system and its corresponding steady-state problem is presented. In particular, by use of a Lyapunov function, the global stability of the constant positive steady state is discussed. For the associated steady state problem, a priori estimates for positive steady states are derived and some non-existence results for non-constant positive steady states are also established when one of the diffusion rates is large enough. Consequently, our results extend and complement the existing ones on this model.
文摘Subject to the homogeneous Neumann boundary condition, a ratio-dependent predator-prey reaction diffusion model is discussed. An improved result for the model is derived, that is, the unique positive constant steady state is the global stability. This is done using the comparison principle and establishing iteration schemes involving positive solutions supremum and infimum. The result indicates that the two species will ultimately distribute homogeneously in space. In fact, the comparison argument and iteration technique to be used in this paper can be applied to some other models. This method deals with the not-existence of a non-constant positive steady state for some reaction diffusion systems, which is rather simple but sufficiently effective.
基金supported by the Cultivation Program for Major Scientific Research Projects of Harbin Institute of Technology(ZDXMPY20180109).
文摘Scalable simulation leveraging real-world data plays an essential role in advancing autonomous driving,owing to its efficiency and applicability in both training and evaluating algorithms.Consequently,there has been increasing attention on generating highly realistic and consistent driving videos,particularly those involving viewpoint changes guided by the control commands or trajectories of ego vehicles.However,current reconstruction approaches,such as Neural Radiance Fields and 3D Gaussian Splatting,frequently suffer from limited generalization and depend on substantial input data.Meanwhile,2D generative models,though capable of producing unknown scenes,still have room for improvement in terms of coherence and visual realism.To overcome these challenges,we introduce GenScene,a world model that synthesizes front-view driving videos conditioned on trajectories.A new temporal module is presented to improve video consistency by extracting the global context of each frame,calculating relationships of frames using these global representations,and fusing frame contexts accordingly.Moreover,we propose an innovative attention mechanism that computes relations of pixels within each frame and pixels in the corresponding window range of the initial frame.Extensive experiments show that our approach surpasses various state-of-the-art models in driving video generation,and the introduced modules contribute significantly to model performance.This work establishes a new paradigm for goal-oriented video synthesis in autonomous driving,which facilitates on-demand simulation to expedite algorithm development.
基金Supported by the National Natural Science Foundation of China(Grant No.12261081).
文摘In this paper,we are concerned with the stability of traveling wavefronts of a Belousov-Zhabotinsky model with mixed nonlocal and degenerate diffusions.Such a system can be used to study the competition among nonlocally diffusive species and degenerately diffusive species.We prove that the traveling wavefronts are exponentially stable,when the initial perturbation around the traveling waves decays exponentially as x→-∞,but in other locations,the initial data can be arbitrarily large.The adopted methods are the weighted energy with the comparison principle and squeezing technique.
基金funding from the European Commission by the Ruralities project(grant agreement no.101060876).
文摘In this paper,we propose a new privacy-aware transmission scheduling algorithm for 6G ad hoc networks.This system enables end nodes to select the optimum time and scheme to transmit private data safely.In 6G dynamic heterogeneous infrastructures,unstable links and non-uniform hardware capabilities create critical issues regarding security and privacy.Traditional protocols are often too computationally heavy to allow 6G services to achieve their expected Quality-of-Service(QoS).As the transport network is built of ad hoc nodes,there is no guarantee about their trustworthiness or behavior,and transversal functionalities are delegated to the extreme nodes.However,while security can be guaranteed in extreme-to-extreme solutions,privacy cannot,as all intermediate nodes still have to handle the data packets they are transporting.Besides,traditional schemes for private anonymous ad hoc communications are vulnerable against modern intelligent attacks based on learning models.The proposed scheme fulfills this gap.Findings show the probability of a successful intelligent attack reduces by up to 65%compared to ad hoc networks with no privacy protection strategy when used the proposed technology.While congestion probability can remain below 0.001%,as required in 6G services.
基金supported by the National Natural Science Foundation of China(Grant No.72161034).
文摘Human motion modeling is a core technology in computer animation,game development,and humancomputer interaction.In particular,generating natural and coherent in-between motion using only the initial and terminal frames remains a fundamental yet unresolved challenge.Existing methods typically rely on dense keyframe inputs or complex prior structures,making it difficult to balance motion quality and plausibility under conditions such as sparse constraints,long-term dependencies,and diverse motion styles.To address this,we propose a motion generation framework based on a frequency-domain diffusion model,which aims to better model complex motion distributions and enhance generation stability under sparse conditions.Our method maps motion sequences to the frequency domain via the Discrete Cosine Transform(DCT),enabling more effective modeling of low-frequency motion structures while suppressing high-frequency noise.A denoising network based on self-attention is introduced to capture long-range temporal dependencies and improve global structural awareness.Additionally,a multi-objective loss function is employed to jointly optimize motion smoothness,pose diversity,and anatomical consistency,enhancing the realism and physical plausibility of the generated sequences.Comparative experiments on the Human3.6M and LaFAN1 datasets demonstrate that our method outperforms state-of-the-art approaches across multiple performance metrics,showing stronger capabilities in generating intermediate motion frames.This research offers a new perspective and methodology for human motion generation and holds promise for applications in character animation,game development,and virtual interaction.
基金supported by NSF of China(11861056)Gansu Provincial Natural Science Foundation(18JR3RA093).
文摘This article is concerned with the existence of traveling wave solutions for a discrete diffusive ratio-dependent predator-prey model. By applying Schauder’s fixed point theorem with the help of suitable upper and lower solutions, we prove that there exists a positive constant c* such that when c > c* , the discrete diffusive predator-prey system admits an invasion traveling wave. The existence of an invasion traveling wave with c = c* is also established by a limiting argument and a delicate analysis of the boundary conditions.Finally, by the asymptotic spreading theory and the comparison principle, the non-existence of invasion traveling waves with speed c < c* is also proved.
文摘In this paper,we consider a diffusive Holling-Tanner predator prey model with Smith growth subject to Neumann boundary condition.We analyze the local stability,exis-tence of a Hopf bifurcation at the co-existence of the equilibrium and stability of bifur-cating periodic solutions of the system in the absence of diffusion.Furthermore the Turing instability and Hopf bifurcation analysis of the system with diffusion are studied.Finally numerical simulations are given to demonstrate the effectiveness of the theoretical analysis.
文摘The dynamical behaviors of a diffusive predator-prey model with Beddington-DeAngelis functional response and disease in the prey is considered in this work. By applying the comparison principle, linearized method, Lyapunov function and iterative method, we are able to achieve sufficient conditions of the permanence, the local stability and global stability of the boundary equilibria and the positive equilibrium, respectively. Our result complements and supplements some known ones.
基金supported by the National Science Foundation of China(No.11801436).
文摘We study local dynamics of a diffusive predator-prey model in a spatially heterogeneous environment,where intrinsic growth rate of the prey is spatially ho-mogeneous,whereas carrying capacity of the habitat is spatially inhomogeneous.In comparison with the existing predator-prey models,the stability of semi-trivial steady state of this model displays distinct properties.For example,for certain intermediate ranges of the death rate of the predator,the semi-trivial steady state can change its stability at least once as the dispersal rate of the prey varies from small to large,while the stability of the semi-trivial steady state is immune from the dispersal rate of the predator.
基金supported by the Natural Science Foundation of Shandong Province,China(Nos.ZR2021MA028 and ZR2021MA025).
文摘In this paper,we study a diffusive predator-prey model with hyperbolic mortality and prey-taxis under homogeneous Neumann boundary condition.We first analyze the influence of prey-taxis on the local stability of constant equilibria.It turns out that prey-taxis has influence on the stability of the unique positive constant equilibrium,but has no influence on the stability of the trivial equilibrium and the semi-trivial equilibrium.We then derive Hopf bifurcation and steady state bifurcation related to prey-taxis,which imply that the prey-taxis plays an important role in the dynamics.
文摘The purpose of this paper is to study the traveling wave solutions of a diffusive predator- prey model with predator saturation and competition functional response. The system admits three equilibria： a zero equilibrium E0, a boundary equilibrium E1 and a posi- tive equilibrium E. under some conditions. We establish the existence of two types of traveling wave solutions which connect E0 and E. and E1 and E., respectively. Our main arguments are based on a simplified shooting method, a sandwich method and constructions of appropriate Lyapunov functions. Our particular interest is to investi- gate the oscillation of both types of traveling wave solutions when they approach the positive equilibrium.
文摘In this paper, spatial patterns of a diffusive predator-prey model with sigmoid （Holling type III） ratio-dependent functional response which concerns the influence of logistic population growth in prey and intra-species competition among predators are investigated. The （local and global） asymptotic stability behavior of the corresponding non- spatial model around the unique positive interior equilibrium point in homogeneous steady state is obtained. In addition, we derive the conditions for Turing instability and the consequent parametric Turing space in spatial domain. The results of spatial pat- tern analysis through numerical simulations are depicted and analyzed. ~rthermore, we perform a series of numerical simulations and find that the proposed model dynamics exhibits complex pattern replication. The feasible results obtained in this paper indicate that the effect of diffusion in Turing instability plays an important role to understand better the pattern formation in ecosystem.
基金supported by the Sichuan Science and Technology Program of China(2018JY0480)the Natural Science Foundation Project of CQ CSTC of China(cstc2015jcyjBX0135)the National Nature Science Fundation of China(61503053)
文摘This article is focusing on a class of multi-delay predator-prey model with feedback controls and prey diffusion. By developing some new analysis methods and using the theory of differential inequalities as well as constructing a suitable Lyapunov function, we establish a set of easily verifiable sufficient conditions which guarantee the permanence of the system and the globally attractivity of positive solution for the predator-prey system.Furthermore, some conditions for the existence, uniqueness and stability of positive periodic solution for the corresponding periodic system are obtained by using the fixed point theory and some new analysis techniques. In additional, some numerical solutions of the equations describing the system are given to verify the obtained criteria are new, general, and easily verifiable. Finally, we still solve numerically the corresponding stochastic predator-prey models with multiplicative noise sources, and obtain some new interesting dynamical behaviors of the system.
基金supported by the National Natural Science Foundation of China(Nos.61906168,62202429 and 62272267)the Zhejiang Provincial Natural Science Foundation of China(No.LY23F020023)the Construction of Hubei Provincial Key Laboratory for Intelligent Visual Monitoring of Hydropower Projects(No.2022SDSJ01)。
文摘Accurately identifying building distribution from remote sensing images with complex background information is challenging.The emergence of diffusion models has prompted the innovative idea of employing the reverse denoising process to distill building distribution from these complex backgrounds.Building on this concept,we propose a novel framework,building extraction diffusion model(BEDiff),which meticulously refines the extraction of building footprints from remote sensing images in a stepwise fashion.Our approach begins with the design of booster guidance,a mechanism that extracts structural and semantic features from remote sensing images to serve as priors,thereby providing targeted guidance for the diffusion process.Additionally,we introduce a cross-feature fusion module(CFM)that bridges the semantic gap between different types of features,facilitating the integration of the attributes extracted by booster guidance into the diffusion process more effectively.Our proposed BEDiff marks the first application of diffusion models to the task of building extraction.Empirical evidence from extensive experiments on the Beijing building dataset demonstrates the superior performance of BEDiff,affirming its effectiveness and potential for enhancing the accuracy of building extraction in complex urban landscapes.
文摘In this paper, a three species diffusive predator-prey model with functional response is studied, where all parameters are time dependent. By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for this system is established.
基金partially supported by the National Natural Science Foundation of China(62271485)the SDHS Science and Technology Project(HS2023B044)
文摘Imputation of missing data has long been an important topic and an essential application for intelligent transportation systems(ITS)in the real world.As a state-of-the-art generative model,the diffusion model has proven highly successful in image generation,speech generation,time series modelling etc.and now opens a new avenue for traffic data imputation.In this paper,we propose a conditional diffusion model,called the implicit-explicit diffusion model,for traffic data imputation.This model exploits both the implicit and explicit feature of the data simultaneously.More specifically,we design two types of feature extraction modules,one to capture the implicit dependencies hidden in the raw data at multiple time scales and the other to obtain the long-term temporal dependencies of the time series.This approach not only inherits the advantages of the diffusion model for estimating missing data,but also takes into account the multiscale correlation inherent in traffic data.To illustrate the performance of the model,extensive experiments are conducted on three real-world time series datasets using different missing rates.The experimental results demonstrate that the model improves imputation accuracy and generalization capability.
基金co-supported by the National Natural Science Foundation of China(Nos.61806219,61876189 and 61703426)the Young Talent Fund of University Association for Science and Technology in Shaanxi,China(Nos.20190108 and 20220106)the Innvation Talent Supporting Project of Shaanxi,China(No.2020KJXX-065)。
文摘Air target intent recognition holds significant importance in aiding commanders to assess battlefield situations and secure a competitive edge in decision-making.Progress in this domain has been hindered by challenges posed by imbalanced battlefield data and the limited robustness of traditional recognition models.Inspired by the success of diffusion models in addressing visual domain sample imbalances,this paper introduces a new approach that utilizes the Markov Transfer Field(MTF)method for time series data visualization.This visualization,when combined with the Denoising Diffusion Probabilistic Model(DDPM),effectively enhances sample data and mitigates noise within the original dataset.Additionally,a transformer-based model tailored for time series visualization and air target intent recognition is developed.Comprehensive experimental results,encompassing comparative,ablation,and denoising validations,reveal that the proposed method achieves a notable 98.86%accuracy in air target intent recognition while demonstrating exceptional robustness and generalization capabilities.This approach represents a promising avenue for advancing air target intent recognition.
基金supported by the National Natural Science Foundation of China(Grant No.62202210).
文摘The application of generative artificial intelligence(AI)is bringing about notable changes in anime creation.This paper surveys recent advancements and applications of diffusion and language models in anime generation,focusing on their demonstrated potential to enhance production efficiency through automation and personalization.Despite these benefits,it is crucial to acknowledge the substantial initial computational investments required for training and deploying these models.We conduct an in-depth survey of cutting-edge generative AI technologies,encompassing models such as Stable Diffusion and GPT,and appraise pivotal large-scale datasets alongside quantifiable evaluation metrics.Review of the surveyed literature indicates the achievement of considerable maturity in the capacity of AI models to synthesize high-quality,aesthetically compelling anime visual images from textual prompts,alongside discernible progress in the generation of coherent narratives.However,achieving perfect long-form consistency,mitigating artifacts like flickering in video sequences,and enabling fine-grained artistic control remain critical ongoing challenges.Building upon these advancements,research efforts have increasingly pivoted towards the synthesis of higher-dimensional content,such as video and three-dimensional assets,with recent studies demonstrating significant progress in this burgeoning field.Nevertheless,formidable challenges endure amidst these advancements.Foremost among these are the substantial computational exigencies requisite for training and deploying these sophisticated models,particularly pronounced in the realm of high-dimensional generation such as video synthesis.Additional persistent hurdles include maintaining spatial-temporal consistency across complex scenes and mitigating ethical considerations surrounding bias and the preservation of human creative autonomy.This research underscores the transformative potential and inherent complexities of AI-driven synergy within the creative industries.We posit that future research should be dedicated to the synergistic fusion of diffusion and autoregressive models,the integration of multimodal inputs,and the balanced consideration of ethical implications,particularly regarding bias and the preservation of human creative autonomy,thereby establishing a robust foundation for the advancement of anime creation and the broader landscape of AI-driven content generation.
基金Supported by the Social Science Foundation of Hebei Province(Grant No.HB23TJ003)the Science Research Project of Hebei Education Department(Grant No.BJK2024197)。
文摘This paper examines an epidemic predator-prey model with prey dispersal and Holling type-II functional response. In this model, it is assumed that the predator population suffers a transmissible disease. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the coexistence equilibrium is addressed. Using Lyapunov functionals and LaSalle's invariance principle, we obtained the sufficient conditions for the global stability of the trivial equilibrium, the predator-extinction equilibrium, the disease-free equilibrium and the coexistence equilibrium, respectively. The paper also includes numerical simulations to illustrate the analytical results.
