A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. B...A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.展开更多
We are interested in the coexistence of three species forming a tritrophic food chain model. Considering a linear grow for the lowest trophic species or prey, and a type III Holling functional response for the middle ...We are interested in the coexistence of three species forming a tritrophic food chain model. Considering a linear grow for the lowest trophic species or prey, and a type III Holling functional response for the middle and highest trophic species (first and second predator respectively). We prove that this model exhibits two small amplitud periodic solutions bifurcating simultaneously each one from one of the two zero-Hopf equilibrium points that the model has adequate values of its parameters. As far as we know, this is the first time that the phenomena appear in the literature related with food chain models.展开更多
Aiming at the spatial pattern phenomenon in biochemical reactions,an enzyme-reaction Sporns-Seelig model with cross-diffusion is chosen as study object.Applying the central manifold theory,normal form method,local Hop...Aiming at the spatial pattern phenomenon in biochemical reactions,an enzyme-reaction Sporns-Seelig model with cross-diffusion is chosen as study object.Applying the central manifold theory,normal form method,local Hopf bifurcation theorem and perturbation theory,we study Turing instability of the spatially homogeneous Hopf bifurcation periodic solutions.At last,the theoretical results are verified by numerical simulations.展开更多
We present a minimal theoretical model for self-sustained oscillations of a thin elastic sheet on a hot plate,induced by thermomechanical coupling.As the plate temperature increases,the sheet’s static deflection beco...We present a minimal theoretical model for self-sustained oscillations of a thin elastic sheet on a hot plate,induced by thermomechanical coupling.As the plate temperature increases,the sheet’s static deflection becomes unstable via a Hopf bifurcation at a critical temperature TC,giving rise to spontaneous periodic motion.Linear stability analysis yields analytical expressions for the critical oscillation temperature TC and the oscillation period at onset.Numerical simulations of the nonlinear equations confirm the bifurcation and reveal how key parameters(stiffness,thermal softening,thermal coupling,etc.)govern the oscillation amplitude and waveform.Finally,we demonstrate that the self-oscillating sheet can perform mechanical work as a heat engine,and we compare its performance to the Carnot efficiency limit.This work provides design principles for thermally driven selfoscillators with potential applications in soft robotics,adaptive structures,and thermal energy harvesting.展开更多
This paper presents the dynamical properties of a discrete-time prey-predator model with refuge in prey under imprecise biological parameters.We consider the refuge concept of prey,which is proportional to the density...This paper presents the dynamical properties of a discrete-time prey-predator model with refuge in prey under imprecise biological parameters.We consider the refuge concept of prey,which is proportional to the density of prey species with interval parameters.The model develops with natural interval parameters since the uncertainties of parameters of any ecological system are a widespread phenomenon in nature.The equilibria of the model are obtained,and the dynamic behaviours of the proposed system are examined.Simulations of the model are performed for different parameters of the model.Numerical simulations show that the proposed discrete model exhibits rich dynamics of a chaotic and complex nature.Our study,through analytical derivation and numerical example,presents the effect of refuge on population dynamics under imprecise biological parameters.展开更多
This study theoretically investigates chaos in a cavity optomechanical system with Coulomb coupling.The system consists of a Fabry-Pérot cavity with a movable mirror,where Coulomb interactions arise from charging...This study theoretically investigates chaos in a cavity optomechanical system with Coulomb coupling.The system consists of a Fabry-Pérot cavity with a movable mirror,where Coulomb interactions arise from charging the two movable mirrors.We examine the chaotic dynamics under the influence of both single and bichromatic laser fields.The single laser field represents a system driven exclusively by the pump field,whereas the bichromatic field represents simultaneous driving by both the pump and probe fields.In addition to conventional chaos-inducing methods through parameter variations,we demonstrate that increasing the Coulomb coupling strength enhances the system’s nonlinearity and induces chaotic behavior.Furthermore,we propose several strategies for generating and controlling chaos,while also identifying the parameter ranges necessary for the resonance of the two mechanical oscillators.Interestingly,when adjusting the driving power in a system driven solely by the pump field,we unexpectedly observe the emergence of high-order sidebands.These findings contribute to the development of chaotic behavior in future cavity optomechanical systems and provide a theoretical basis for applications in physical random number generation and secure communication.展开更多
This paper studies a dual-channel green supply chain consisting of one manufacturer and one retailer in presence of government green subsidy and cap-and-trade regulation policies.We first develop and analyze a single-...This paper studies a dual-channel green supply chain consisting of one manufacturer and one retailer in presence of government green subsidy and cap-and-trade regulation policies.We first develop and analyze a single-period Stackelberg and a multi-period dynamic Stackelberg game models respectively with consistent pricing strategy.Subsequently,we extend these two game models by utilizing an inconsistent pricing strategy.The optimal solutions for the single-period Stackelberg game models in both scenarios are derived by means of the backward induction approach.Moreover,the existence and local asymptotic stability of the equilibrium points of the multi-period dynamic Stackelberg game models are examined,and the complex dynamics of chain members'long-term strategy evolution are investigated through chaos theory and numerical simulation.Additionally,the variable feedback control and time-delay feedback control method are utilized to eliminate system chaos respectively.The results indicate that(i)The excessive fast adjustment speeds by the manufacturer have a destabilizing effect on the stability of the Nash equilibrium point.(ii)The manufacturer's profits are improved with green subsidy degree increases,while its impact on the retailer's profits depends on certain parameter conditions,and the high carbon trading price is disadvantage to both chain members.(iii)The system's motion can transition from a steady state to a chaotic period through period-doubling or Neimark–Sacker bifurcations.(iv)The system's steady state is conducive to the manufacturer,while the retailer can benefit from the system's periodic cycles.Furthermore,both chain members'profits are declined when the system becomes chaotic.Lastly,the variable feedback and time-delay feedback control method can effectively eliminate system chaos.展开更多
This article is devoted to the study of the neural mechanisms of the binary substance of the brain in the process of creating,presenting and evaluating new approaches,methods and tools in the field of art.The interrel...This article is devoted to the study of the neural mechanisms of the binary substance of the brain in the process of creating,presenting and evaluating new approaches,methods and tools in the field of art.The interrelation and interdependence of genetically determined neural structures in the subcortical sphere and the neocortex in the creative process are shown.The scientific interpretation of the concepts of trance and bifurcation as mechanisms for the emergence of a new approach,method,and means for an innovator is given,and the peculiarities of perception and identification of innovations by art connoisseurs are characterized.展开更多
0 INTRODUCTION Natural geomaterials,including soils and rocks,are invariably exposed to intricate stress conditions,in addition to water pressure,in various engineering contexts such as foundation treatment,mining,and...0 INTRODUCTION Natural geomaterials,including soils and rocks,are invariably exposed to intricate stress conditions,in addition to water pressure,in various engineering contexts such as foundation treatment,mining,and tunneling.These geomaterials frequently contain numerous fractures,which significantly influence hydrological dynamics as water permeates through them,leading to processes like expansion and bifurcation(Shu et al.,2023;Tran and Jha,2021;Lei et al.,2017;Wang et al.,2015).展开更多
This paper deeply introduces a brand-new research method for the synchronous characteristics of DC microgrid bus voltage and an improved synchronous control strategy.This method mainly targets the problem of bus volta...This paper deeply introduces a brand-new research method for the synchronous characteristics of DC microgrid bus voltage and an improved synchronous control strategy.This method mainly targets the problem of bus voltage oscillation caused by the bifurcation behavior of DC microgrid converters.Firstly,the article elaborately establishes a mathematical model of a single distributed power source with hierarchical control.On this basis,a smallworld network model that can better adapt to the topology structure of DC microgrids is further constructed.Then,a voltage synchronization analysis method based on the main stability function is proposed,and the synchronous characteristics of DC bus voltage are deeply studied by analyzing the size of the minimum non-zero eigenvalue.In view of the situation that the line coupling strength between distributed power sources is insufficient to achieve bus voltage synchronization,this paper innovatively proposes a new improved adaptive controller to effectively control voltage synchronization.And the convergence of the designed controller is strictly proved by using Lyapunov’s stability theorem.Finally,the effectiveness and feasibility of the designed controller in this paper are fully verified through detailed simulation experiments.After comparative analysis with the traditional adaptive controller,it is found that the newly designed controller can make the bus voltages of each distributed power source achieve synchronization more quickly,and is significantly superior to the traditional adaptive controller in terms of anti-interference performance.展开更多
In a fractal zeta universe of bifurcated, ripped spacetime, the Millikan experiment, the quantum Hall effect, atmospheric clouds and universe clouds are shown to be self-similar with mass ratio of about 1020. Chaotic ...In a fractal zeta universe of bifurcated, ripped spacetime, the Millikan experiment, the quantum Hall effect, atmospheric clouds and universe clouds are shown to be self-similar with mass ratio of about 1020. Chaotic one-dimensional period-doublings as iterated hyperelliptic-elliptic curves are used to explain n-dim Kepler- and Coulomb singularities. The cosmic microwave background and cosmic rays are explained as bifurcated, ripped spacetime tensile forces. First iterated binary tree cloud cycles are related to emissions 1…1000 GHz. An interaction-independent universal vacuum density allows to predict large area correlated cosmic rays in quantum Hall experiments which would generate local nuclear disintegration stars, enhanced damage of layers and enhanced air ionization. A self-similarity between conductivity plateau and atmospheric clouds is extended to correlations in atmospheric layer, global temperature and climate.展开更多
We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portrai...We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portraits of the unperturbed system are found. Then, using the first order Melnikov function, Hopf bifurcation problem of the perturbed system is investigated, and an upper bound for the function is obtained near the origin.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
This paper is concerned with a diffusive Ivlev-type predator-prey system with Smith growth and a protection zone. By discussing the existence and non-existence of positive solutions,we discover that the incorporation ...This paper is concerned with a diffusive Ivlev-type predator-prey system with Smith growth and a protection zone. By discussing the existence and non-existence of positive solutions,we discover that the incorporation of the Smith growth function has enabled us to obtain a more precise criterion when judging the structure of bifurcation solutions, and determine a critical size for the protection zone. The results indicate that if the size of the protection zone is below the critical patch size, then the system has no positive steady state solution for excessively high intrinsic growth rates of predators. Conversely, if the size of the protection zone exceeds the critical patch size, there exists positive steady state solution regardless of how large the intrinsic growth rate of the predators is.展开更多
Since the method of discretizing memristors was proposed,discrete memristors(DMs)have become a very important topic in recent years.However,there has been little research on non-autonomous discrete memristors(NDMs)and...Since the method of discretizing memristors was proposed,discrete memristors(DMs)have become a very important topic in recent years.However,there has been little research on non-autonomous discrete memristors(NDMs)and their applications.Therefore,in this paper,a new NDM is constructed,and a non-autonomous hyperchaotic map is proposed by connecting this non-autonomous memristor in parallel with an autonomous memristor.This map exhibits complex dynamical behaviors,including infinitely many fixed points,initial-boosted attractors,initial-boosted bifurcations,and the size of the attractors being controlled by the initial value.In addition,a simple pseudo-random number generator(PRNG)was designed using the non-autonomous hyperchaotic map,and the pseudo-random numbers(PRNs)generated by it were tested using the National Institute of Standards and Technology(NIST)SP800-22 test suite.Finally,the non-autonomous hyperchaotic map is implemented on the STM32 hardware experimental platform.展开更多
The dynamic behaviors of a large-scale ring neural network with a triangular coupling structure are investigated.The characteristic equation of the high-dimensional system using Coate’s flow graph method is calculate...The dynamic behaviors of a large-scale ring neural network with a triangular coupling structure are investigated.The characteristic equation of the high-dimensional system using Coate’s flow graph method is calculated.Time delay is selected as the bifurcation parameter,and sufficient conditions for stability and Hopf bifurcation are derived.It is found that the connection coefficient and time delay play a crucial role in the dynamic behaviors of the model.Furthermore,a phase diagram of multiple equilibrium points with one saddle point and two stable nodes is presented.Finally,the effectiveness of the theory is verified through simulation results.展开更多
In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensa...In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensate. Based on the bifurcation theory, we proved the existence of solitary and periodic solutions. The methods we take are the trial equation method and the complete discrimination system for polynomial method. Therefore, we obtain the exact chirped solutions, which are more abundant in type and quantity than the existing results, so that the equation has more profound physical significance. These two methods are rigorously mathematical derivation and calculations, rather than based on certain conditional assumptions. In addition, we give some specific parameters to graphing the motion of the solutions, which helps to understand the propagation of nonlinear waves in fiber optic systems.展开更多
The construction of bifurcated tunnels is essential to advancing urban infrastructure systems,as they conserve land,reduce carbon emissions,and optimize traffic.However,the bifurcation structure of the parallel conflu...The construction of bifurcated tunnels is essential to advancing urban infrastructure systems,as they conserve land,reduce carbon emissions,and optimize traffic.However,the bifurcation structure of the parallel confluence section of such tunnels poses significant challenges in the design and operation of the tunnel ventilation system,in terms of both the internal and external environment.In this work,the flow and loss characteristics of parallel confluence sections are studied with numerical simulations and model experiments.The influences of the confluence ratio q and the confluence angle O on the flow characteristics and loss mechanisms of the parallel confluence section are revealed theoretically.The results indicate that when q is small,the high-velocity airflow from the mainline entrains the low-speed airflow from the ramp,leading to flow separation at the upper connection between the parallel section and the gradual transition section;when q is large,the high-velocity airflow from the ramp entrains the low-speed airflow from the mainline,resulting in flow separation on the side of the confluence section adjacent to the mainline.Additionally,the mismatch between the airflow ratio Q and cross-sectional area ratio of the mainline tunnel and the ramp prior to confluence enhances the jet entrainment effect,increases the curvature of the streamline,expands the range of the flow separation area,and generates higher confluence loss coefficients|K_(13)|and|K_(23)|of the mainline and the ramp.For small q,|K_(13)|,and|K_(23)|,remain relatively constant with respect toθ,whereas for large q,both|K_(13)|and|K_(23)|decrease asθincreases.Finally,a semi-empirical formula is proposed to predict the loss coefficients for parallel bifurcated tunnels with confluence angles ranging from 5°to 15°.This study provides insights into the aerodynamic behaviour and loss mechanisms in bifurcated tunnels,offering guidelines for enhancing the efficiency of tunnel ventilation systems in tunnel-like underground infrastructure.展开更多
In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system w...In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results.展开更多
Model-free,data-driven prediction of chaotic motions is a long-standing challenge in nonlinear science.Stimulated by the recent progress in machine learning,considerable attention has been given to the inference of ch...Model-free,data-driven prediction of chaotic motions is a long-standing challenge in nonlinear science.Stimulated by the recent progress in machine learning,considerable attention has been given to the inference of chaos by the technique of reservoir computing(RC).In particular,by incorporating a parameter-control channel into the standard RC,it is demonstrated that the machine is able to not only replicate the dynamics of the training states,but also infer new dynamics not included in the training set.The new machine-learning scheme,termed parameter-aware RC,opens up new avenues for data-based analysis of chaotic systems,and holds promise for predicting and controlling many real-world complex systems.Here,using typical chaotic systems as examples,we give a comprehensive introduction to this powerful machine-learning technique,including the algorithm,the implementation,the performance,and the open questions calling for further studies.展开更多
基金Supported by the National Natural Science Foundation of China (10961017)"Qinglan" Talent Programof Lanzhou Jiaotong University (QL-05-20A)
文摘A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.
文摘We are interested in the coexistence of three species forming a tritrophic food chain model. Considering a linear grow for the lowest trophic species or prey, and a type III Holling functional response for the middle and highest trophic species (first and second predator respectively). We prove that this model exhibits two small amplitud periodic solutions bifurcating simultaneously each one from one of the two zero-Hopf equilibrium points that the model has adequate values of its parameters. As far as we know, this is the first time that the phenomena appear in the literature related with food chain models.
基金supported by Scientific Research and Innovation Fund for PhD Student:Research on the bifurcation problems of diffusive oncolytic virotherapy system(No.3072022CFJ2401).
文摘Aiming at the spatial pattern phenomenon in biochemical reactions,an enzyme-reaction Sporns-Seelig model with cross-diffusion is chosen as study object.Applying the central manifold theory,normal form method,local Hopf bifurcation theorem and perturbation theory,we study Turing instability of the spatially homogeneous Hopf bifurcation periodic solutions.At last,the theoretical results are verified by numerical simulations.
基金supported by the Guangdong Basic and Applied Basic Research Foundation(Grant Nos.2025B1515020077 and 2024A15150301-39)the National Natural Science Foundation of China(Grant No.12205138)the Shenzhen Science and Technology Innovation Committee(Grant No.JCYJ2022-0530113206015).
文摘We present a minimal theoretical model for self-sustained oscillations of a thin elastic sheet on a hot plate,induced by thermomechanical coupling.As the plate temperature increases,the sheet’s static deflection becomes unstable via a Hopf bifurcation at a critical temperature TC,giving rise to spontaneous periodic motion.Linear stability analysis yields analytical expressions for the critical oscillation temperature TC and the oscillation period at onset.Numerical simulations of the nonlinear equations confirm the bifurcation and reveal how key parameters(stiffness,thermal softening,thermal coupling,etc.)govern the oscillation amplitude and waveform.Finally,we demonstrate that the self-oscillating sheet can perform mechanical work as a heat engine,and we compare its performance to the Carnot efficiency limit.This work provides design principles for thermally driven selfoscillators with potential applications in soft robotics,adaptive structures,and thermal energy harvesting.
文摘This paper presents the dynamical properties of a discrete-time prey-predator model with refuge in prey under imprecise biological parameters.We consider the refuge concept of prey,which is proportional to the density of prey species with interval parameters.The model develops with natural interval parameters since the uncertainties of parameters of any ecological system are a widespread phenomenon in nature.The equilibria of the model are obtained,and the dynamic behaviours of the proposed system are examined.Simulations of the model are performed for different parameters of the model.Numerical simulations show that the proposed discrete model exhibits rich dynamics of a chaotic and complex nature.Our study,through analytical derivation and numerical example,presents the effect of refuge on population dynamics under imprecise biological parameters.
基金supported by Young Talents from Longyuan,Gansu Province(Liwei Liu),the Fundamental Research Funds for the Central Universities,Northwest Minzu University(Grant No.31920230134)Teaching Achievement Cultivation Project of Gansu Province Department of Education(Grant No.2022GSJXCGPY-46)+1 种基金Special research topic on curriculum and teaching materials for primary,secondary and higher schools,Gansu Province Department of Education(Grant No.GSJC-Y2024204)Quality improvement project for undergraduate talent training,Northwest Minzu University(Grant Nos.2024YBJG-04 and 2024FCTD-03).
文摘This study theoretically investigates chaos in a cavity optomechanical system with Coulomb coupling.The system consists of a Fabry-Pérot cavity with a movable mirror,where Coulomb interactions arise from charging the two movable mirrors.We examine the chaotic dynamics under the influence of both single and bichromatic laser fields.The single laser field represents a system driven exclusively by the pump field,whereas the bichromatic field represents simultaneous driving by both the pump and probe fields.In addition to conventional chaos-inducing methods through parameter variations,we demonstrate that increasing the Coulomb coupling strength enhances the system’s nonlinearity and induces chaotic behavior.Furthermore,we propose several strategies for generating and controlling chaos,while also identifying the parameter ranges necessary for the resonance of the two mechanical oscillators.Interestingly,when adjusting the driving power in a system driven solely by the pump field,we unexpectedly observe the emergence of high-order sidebands.These findings contribute to the development of chaotic behavior in future cavity optomechanical systems and provide a theoretical basis for applications in physical random number generation and secure communication.
基金Project supported by the General Projects of Philosophy and Social Science Research in Jiangsu Province Universities(Grant No.2024SJYB1101)the National Youth Fund Guidance Project of Jiangsu University of Science and Technology(Zhangjiagang Campus)+2 种基金the Special Project for Cultivating Leading Talents in Philosophy and Social Science Planning of Zhejiang Province,China(Grant No.22YJRC14ZD)the Shanghai Pujiang Program(Grant No.2021PJC066)the National Natural Science Foundation of China(Grant No.72302142)。
文摘This paper studies a dual-channel green supply chain consisting of one manufacturer and one retailer in presence of government green subsidy and cap-and-trade regulation policies.We first develop and analyze a single-period Stackelberg and a multi-period dynamic Stackelberg game models respectively with consistent pricing strategy.Subsequently,we extend these two game models by utilizing an inconsistent pricing strategy.The optimal solutions for the single-period Stackelberg game models in both scenarios are derived by means of the backward induction approach.Moreover,the existence and local asymptotic stability of the equilibrium points of the multi-period dynamic Stackelberg game models are examined,and the complex dynamics of chain members'long-term strategy evolution are investigated through chaos theory and numerical simulation.Additionally,the variable feedback control and time-delay feedback control method are utilized to eliminate system chaos respectively.The results indicate that(i)The excessive fast adjustment speeds by the manufacturer have a destabilizing effect on the stability of the Nash equilibrium point.(ii)The manufacturer's profits are improved with green subsidy degree increases,while its impact on the retailer's profits depends on certain parameter conditions,and the high carbon trading price is disadvantage to both chain members.(iii)The system's motion can transition from a steady state to a chaotic period through period-doubling or Neimark–Sacker bifurcations.(iv)The system's steady state is conducive to the manufacturer,while the retailer can benefit from the system's periodic cycles.Furthermore,both chain members'profits are declined when the system becomes chaotic.Lastly,the variable feedback and time-delay feedback control method can effectively eliminate system chaos.
文摘This article is devoted to the study of the neural mechanisms of the binary substance of the brain in the process of creating,presenting and evaluating new approaches,methods and tools in the field of art.The interrelation and interdependence of genetically determined neural structures in the subcortical sphere and the neocortex in the creative process are shown.The scientific interpretation of the concepts of trance and bifurcation as mechanisms for the emergence of a new approach,method,and means for an innovator is given,and the peculiarities of perception and identification of innovations by art connoisseurs are characterized.
基金supported by the National Key R&D Program of China(No.2023YFC3008401)the National Natural Science Foundation of China(No.42372307)。
文摘0 INTRODUCTION Natural geomaterials,including soils and rocks,are invariably exposed to intricate stress conditions,in addition to water pressure,in various engineering contexts such as foundation treatment,mining,and tunneling.These geomaterials frequently contain numerous fractures,which significantly influence hydrological dynamics as water permeates through them,leading to processes like expansion and bifurcation(Shu et al.,2023;Tran and Jha,2021;Lei et al.,2017;Wang et al.,2015).
基金supported by the National Natural Science Foundation of China(Nos.51767017 and 51867015)the Basic Research and Innovation Group Project of Gansu(No.18JR3RA13)the Major Science and Technology Project of Gansu(No.19ZD2GA003).
文摘This paper deeply introduces a brand-new research method for the synchronous characteristics of DC microgrid bus voltage and an improved synchronous control strategy.This method mainly targets the problem of bus voltage oscillation caused by the bifurcation behavior of DC microgrid converters.Firstly,the article elaborately establishes a mathematical model of a single distributed power source with hierarchical control.On this basis,a smallworld network model that can better adapt to the topology structure of DC microgrids is further constructed.Then,a voltage synchronization analysis method based on the main stability function is proposed,and the synchronous characteristics of DC bus voltage are deeply studied by analyzing the size of the minimum non-zero eigenvalue.In view of the situation that the line coupling strength between distributed power sources is insufficient to achieve bus voltage synchronization,this paper innovatively proposes a new improved adaptive controller to effectively control voltage synchronization.And the convergence of the designed controller is strictly proved by using Lyapunov’s stability theorem.Finally,the effectiveness and feasibility of the designed controller in this paper are fully verified through detailed simulation experiments.After comparative analysis with the traditional adaptive controller,it is found that the newly designed controller can make the bus voltages of each distributed power source achieve synchronization more quickly,and is significantly superior to the traditional adaptive controller in terms of anti-interference performance.
文摘In a fractal zeta universe of bifurcated, ripped spacetime, the Millikan experiment, the quantum Hall effect, atmospheric clouds and universe clouds are shown to be self-similar with mass ratio of about 1020. Chaotic one-dimensional period-doublings as iterated hyperelliptic-elliptic curves are used to explain n-dim Kepler- and Coulomb singularities. The cosmic microwave background and cosmic rays are explained as bifurcated, ripped spacetime tensile forces. First iterated binary tree cloud cycles are related to emissions 1…1000 GHz. An interaction-independent universal vacuum density allows to predict large area correlated cosmic rays in quantum Hall experiments which would generate local nuclear disintegration stars, enhanced damage of layers and enhanced air ionization. A self-similarity between conductivity plateau and atmospheric clouds is extended to correlations in atmospheric layer, global temperature and climate.
基金supported by the National Natural Science Foundations of China(12371171)and the Natural Science Foundation of Jiangsu Province(BK20221339).
文摘We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portraits of the unperturbed system are found. Then, using the first order Melnikov function, Hopf bifurcation problem of the perturbed system is investigated, and an upper bound for the function is obtained near the origin.
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.
基金Supported by the National Natural Science Foundation of China(Grant No.12161080)。
文摘This paper is concerned with a diffusive Ivlev-type predator-prey system with Smith growth and a protection zone. By discussing the existence and non-existence of positive solutions,we discover that the incorporation of the Smith growth function has enabled us to obtain a more precise criterion when judging the structure of bifurcation solutions, and determine a critical size for the protection zone. The results indicate that if the size of the protection zone is below the critical patch size, then the system has no positive steady state solution for excessively high intrinsic growth rates of predators. Conversely, if the size of the protection zone exceeds the critical patch size, there exists positive steady state solution regardless of how large the intrinsic growth rate of the predators is.
基金supported by the National Natural Science Foundation of China(Grant No.62071411).
文摘Since the method of discretizing memristors was proposed,discrete memristors(DMs)have become a very important topic in recent years.However,there has been little research on non-autonomous discrete memristors(NDMs)and their applications.Therefore,in this paper,a new NDM is constructed,and a non-autonomous hyperchaotic map is proposed by connecting this non-autonomous memristor in parallel with an autonomous memristor.This map exhibits complex dynamical behaviors,including infinitely many fixed points,initial-boosted attractors,initial-boosted bifurcations,and the size of the attractors being controlled by the initial value.In addition,a simple pseudo-random number generator(PRNG)was designed using the non-autonomous hyperchaotic map,and the pseudo-random numbers(PRNs)generated by it were tested using the National Institute of Standards and Technology(NIST)SP800-22 test suite.Finally,the non-autonomous hyperchaotic map is implemented on the STM32 hardware experimental platform.
基金Supported by Natural Science Foundation of Shandong Province of China(Grant Nos.ZR2020MF080 and ZR2020MF065).
文摘The dynamic behaviors of a large-scale ring neural network with a triangular coupling structure are investigated.The characteristic equation of the high-dimensional system using Coate’s flow graph method is calculated.Time delay is selected as the bifurcation parameter,and sufficient conditions for stability and Hopf bifurcation are derived.It is found that the connection coefficient and time delay play a crucial role in the dynamic behaviors of the model.Furthermore,a phase diagram of multiple equilibrium points with one saddle point and two stable nodes is presented.Finally,the effectiveness of the theory is verified through simulation results.
文摘In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensate. Based on the bifurcation theory, we proved the existence of solitary and periodic solutions. The methods we take are the trial equation method and the complete discrimination system for polynomial method. Therefore, we obtain the exact chirped solutions, which are more abundant in type and quantity than the existing results, so that the equation has more profound physical significance. These two methods are rigorously mathematical derivation and calculations, rather than based on certain conditional assumptions. In addition, we give some specific parameters to graphing the motion of the solutions, which helps to understand the propagation of nonlinear waves in fiber optic systems.
基金supported by the National Natural Science Foundation of China(Nos.52408439 and 52478422)the Natural Science Basic Research Program of Shaanxi(No.2023-JC-YB-378),China+3 种基金the Young Talent Fund of Xi'an Association for Science and Technology(No.0959202513050),Chinathe Fundamental Research Funds for the Zhejiang Provincial Universities(No.226-2024-00099),Chinathe Postdoctoral Fellowship Program of China Postdoctoral Science Foundation(No.GZC20241518)the Xi'an Shiyou University Graduate Student Innovation Fund Program(No.YCX2512041),China.
文摘The construction of bifurcated tunnels is essential to advancing urban infrastructure systems,as they conserve land,reduce carbon emissions,and optimize traffic.However,the bifurcation structure of the parallel confluence section of such tunnels poses significant challenges in the design and operation of the tunnel ventilation system,in terms of both the internal and external environment.In this work,the flow and loss characteristics of parallel confluence sections are studied with numerical simulations and model experiments.The influences of the confluence ratio q and the confluence angle O on the flow characteristics and loss mechanisms of the parallel confluence section are revealed theoretically.The results indicate that when q is small,the high-velocity airflow from the mainline entrains the low-speed airflow from the ramp,leading to flow separation at the upper connection between the parallel section and the gradual transition section;when q is large,the high-velocity airflow from the ramp entrains the low-speed airflow from the mainline,resulting in flow separation on the side of the confluence section adjacent to the mainline.Additionally,the mismatch between the airflow ratio Q and cross-sectional area ratio of the mainline tunnel and the ramp prior to confluence enhances the jet entrainment effect,increases the curvature of the streamline,expands the range of the flow separation area,and generates higher confluence loss coefficients|K_(13)|and|K_(23)|of the mainline and the ramp.For small q,|K_(13)|,and|K_(23)|,remain relatively constant with respect toθ,whereas for large q,both|K_(13)|and|K_(23)|decrease asθincreases.Finally,a semi-empirical formula is proposed to predict the loss coefficients for parallel bifurcated tunnels with confluence angles ranging from 5°to 15°.This study provides insights into the aerodynamic behaviour and loss mechanisms in bifurcated tunnels,offering guidelines for enhancing the efficiency of tunnel ventilation systems in tunnel-like underground infrastructure.
基金Supported by the National Natural Science Foundation of China(12071162)the Natural Science Foundation of Fujian Province(2021J01302)the Fundamental Research Funds for the Central Universities(ZQN-802).
文摘In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results.
基金Project supported by the National Natural Science Foundation of China(Grant No.12275165)XGW was also supported by the Fundamental Research Funds for the Central Universities(Grant No.GK202202003).
文摘Model-free,data-driven prediction of chaotic motions is a long-standing challenge in nonlinear science.Stimulated by the recent progress in machine learning,considerable attention has been given to the inference of chaos by the technique of reservoir computing(RC).In particular,by incorporating a parameter-control channel into the standard RC,it is demonstrated that the machine is able to not only replicate the dynamics of the training states,but also infer new dynamics not included in the training set.The new machine-learning scheme,termed parameter-aware RC,opens up new avenues for data-based analysis of chaotic systems,and holds promise for predicting and controlling many real-world complex systems.Here,using typical chaotic systems as examples,we give a comprehensive introduction to this powerful machine-learning technique,including the algorithm,the implementation,the performance,and the open questions calling for further studies.
