This article proposes a non-ideal flux-controlled memristor with a bisymmetric sawtooth piecewise function, and a new multi-wing memristive chaotic system(MMCS) based on the memristor is generated. Compared with other...This article proposes a non-ideal flux-controlled memristor with a bisymmetric sawtooth piecewise function, and a new multi-wing memristive chaotic system(MMCS) based on the memristor is generated. Compared with other existing MMCSs, the most eye-catching point of the proposed MMCS is that the amplitude of the wing will enlarge towards the poles as the number of wings increases. Diverse coexisting attractors are numerically found in the MMCS, including chaos,quasi-period, and stable point. The circuits of the proposed memristor and MMCS are designed and the obtained results demonstrate their validity and reliability.展开更多
A novel 5-dimensional（5D） memristive chaotic system is proposed, in which multi-scroll hidden attractors and multiwing hidden attractors can be observed on different phase planes. The dynamical system has multiple l...A novel 5-dimensional（5D） memristive chaotic system is proposed, in which multi-scroll hidden attractors and multiwing hidden attractors can be observed on different phase planes. The dynamical system has multiple lines of equilibria or no equilibrium when the system parameters are appropriately selected, and the multi-scroll hidden attractors and multi-wing hidden attractors have nothing to do with the system equilibria. Particularly, the numbers of multi-scroll hidden attractors and multi-wing hidden attractors are sensitive to the transient simulation time and the initial values. Dynamical properties of the system, such as phase plane, time series, frequency spectra, Lyapunov exponent, and Poincar′e map, are studied in detail. In addition, a state feedback controller is designed to select multiple hidden attractors within a long enough simulation time. Finally, an electronic circuit is realized in Pspice, and the experimental results are in agreement with the numerical ones.展开更多
This paper aims at developing a novel method of constructing a class of multi-wing chaotic and hyperchaotic system by introducing a unified step function. In order to overcome the essential difficulties in iteratively...This paper aims at developing a novel method of constructing a class of multi-wing chaotic and hyperchaotic system by introducing a unified step function. In order to overcome the essential difficulties in iteratively adjusting multiple parameters of conventional multi-parameter control, this paper introduces a unified step function controlled by a single parameter for constructing various multi-wing chaotic and hyperchaotic systems. In particular, to the best of the authors＇ knowledge, this is also the first time to find a non-equilibrium multi-wing hyperchaotic system by means of the unified step function control. According to the heteroclinic loop Shilnikov theorem, some properties for multi-wing attractors and its chaos mechanism are further discussed and analyzed. A circuit for multi-wing systems is designed and implemented for demonstration, which verifies the effectiveness of the proposed approach.展开更多
The catastrophic rockslide,which frequently triggers numerous severe disasters worldwide,has drawn much attention globally;however,understanding the initiation mechanism of catastrophic rockslides in the absence of ty...The catastrophic rockslide,which frequently triggers numerous severe disasters worldwide,has drawn much attention globally;however,understanding the initiation mechanism of catastrophic rockslides in the absence of typical single triggering factors related to strong seismic activity or torrential precipitation continues to be challenging within the global scientific community.This study aims to determine the mechanism of the three largest catastrophic rockslides in the eastern Tibetan Plateau,Yigong,Xinmo,and Baige,over the past 20 years using field investigation,remote sensing,and runoff analysis.Instead of the conventional driving factors of heavy rainfall and strong earthquakes,the multi-wing butterfly effects(MWBE)of climatic factors and weak earthquakes are for the first time identified as drivers of the catastrophic rockslide disasters.First,strong tectonic uplift,fast fluvial incision,high-density faults,and large regional water confluence formed the slopes in the critical regime,creating the source conditions of rockslide.Second,the MWBE of early dry-heat events and antecedent rainfall,combined with imminent weak earthquakes,initiated rockslide.Third,the delayed amplified runoff moving toward the sliding surface and lowering the strength of the locking-rock segment constituted the fundamental mechanism of the MWBE on rockslide.The catastrophic rockslide was ultimately inferred to be a nonlinear chaotic process;however,prediction and forecasting of rockslide based on the MWBE in the early stages are possible and essential.This finding presents a new perspective concerning forecasting progressive landslides.展开更多
The complexities of multi-wing chaotic systems based on the modified Chen system and a multi-segment quadratic function are investigated by employing the statistical complexity measure （SCM） and the spectral entropy...The complexities of multi-wing chaotic systems based on the modified Chen system and a multi-segment quadratic function are investigated by employing the statistical complexity measure （SCM） and the spectral entropy （SE） algorithm. How to choose the parameters of the SCM and SE algorithms is discussed. The results show that the complexity of the multi-wing chaotic system does not increase as the number of wings increases, and it is consistent with the results of the Grassberger-Procaccia （GP） algorithm and the largest Lyapunov exponent （LLE） of the multi-wing chaotic system.展开更多
This study systematically investigates the attractor characteristics of harmonic solitons in a passively modelocked fiber laser.Through comprehensive analysis in both time and frequency domains,we examine the evolutio...This study systematically investigates the attractor characteristics of harmonic solitons in a passively modelocked fiber laser.Through comprehensive analysis in both time and frequency domains,we examine the evolution of pulse width,spectral bandwidth,and energy across different harmonic orders.The results demonstrate typical soliton attractor behaviors,including attractiveness,dissipativity,and self-organization.In the transition regions between harmonic orders,breathing harmonic soliton states are captured using the time-stretched dispersive Fourier transform.By comparing the breathing dynamics with the stable states,the existence and self-organizing nature of soliton attractors are further confirmed.Finally,harmonic soliton attractors are employed as programmable light sources to achieve ternary optical coding.展开更多
In this paper, we consider the existence of pullback random exponential attractor for non-autonomous random reaction-diffusion equation driven by nonlinear colored noise defined onR^(N) . The key steps of the proof ar...In this paper, we consider the existence of pullback random exponential attractor for non-autonomous random reaction-diffusion equation driven by nonlinear colored noise defined onR^(N) . The key steps of the proof are the tails estimate and to demonstrate the Lipschitz continuity and random squeezing property of the solution for the equation defined on R^(N) .展开更多
In this article,the global attractors of 2D g-Navier-Stokes equations are obtained in the space of C_(Hg) and CVg respectively.When the external force f is sufficiently small,the studies indicate that the global attra...In this article,the global attractors of 2D g-Navier-Stokes equations are obtained in the space of C_(Hg) and CVg respectively.When the external force f is sufficiently small,the studies indicate that the global attractor in C_(Hg) is equal to the global attractor in C_(Vg).展开更多
Existing chaotic encryption schemes primarily focus on single types of images,making the design of hybrid image encryption schemes more suitable for practical applications.In this paper,a hyperchaotic map with a spher...Existing chaotic encryption schemes primarily focus on single types of images,making the design of hybrid image encryption schemes more suitable for practical applications.In this paper,a hyperchaotic map with a spherical attractor is proposed,which is constructed using spherical coordinates.Dynamical analyses reveal that the hyperchaotic map exhibits global hyperchaos and high complexity,making it capable of generating more complex chaotic sequences suitable for image encryption.A hybrid encryption scheme based on a hyperchaotic map is proposed for two-dimensional(2D)images,three-dimensional(3D)models,and 3D point clouds.Firstly,the pixels of 2D image and the coordinate data of 3D image are fused into a plaintext cube,which is combined with Hash-512 to obtain the initial value of the hyperchaotic map.Chaotic sequences are utilized for cube space internal confusion and dynamic cross-diffusion.The encrypted images demonstrate high information entropy,and the test results show that the encryption scheme effectively protects the images.The proposed hybrid image encryption scheme provides an efficient solution for securing various types of images.展开更多
The paper is devoted to establishing the long-time behavior of solutions to the extensible beam equation with rotational inertia and nonlocal strong damping.Within the theory of asymptotical smoothness,we investigate ...The paper is devoted to establishing the long-time behavior of solutions to the extensible beam equation with rotational inertia and nonlocal strong damping.Within the theory of asymptotical smoothness,we investigate the existence of the attractor by using the contractive function method and more detailed estimates.展开更多
This paper proposes a universal impulse-function-based method for extending discrete chaotic maps,enabling flexible construction of multicavity chaotic attractors.The proposed method achieves one-directional(1D)/two-d...This paper proposes a universal impulse-function-based method for extending discrete chaotic maps,enabling flexible construction of multicavity chaotic attractors.The proposed method achieves one-directional(1D)/two-directional(2D)extensions without introducing additional nonlinear terms or altering system stability.Theoretically,the cavity quantity in arbitrary directions is controlled by adjusting impulse levels N,while the amplitude regulation is implemented through modifications to the proportionality parameter r.Theoretical analyses,including Lyapunov exponents(LEs)and bifurcation diagrams,are conducted,confirming that the extended maps retain the intrinsic dynamics of five rational map classes.The field-programmable gate array(FPGA)implementation results are consistent with the numerical simulation results,verifying the correctness of the theoretical analysis.The method enables the expansion of unipolar attractors and enhances entropy metrics,offering a robust framework for applications in secure communication,encryption,and chaos-based technologies.展开更多
The Rössler attractor model is an important model that provides valuable insights into the behavior of chaotic systems in real life and is applicable in understanding weather patterns,biological systems,and secur...The Rössler attractor model is an important model that provides valuable insights into the behavior of chaotic systems in real life and is applicable in understanding weather patterns,biological systems,and secure communications.So,this work aims to present the numerical performances of the nonlinear fractional Rössler attractor system under Caputo derivatives by designing the numerical framework based on Ultraspherical wavelets.The Caputo fractional Rössler attractor model is simulated into two categories,(i)Asymmetric and(ii)Symmetric.The Ultraspherical wavelets basis with suitable collocation grids is implemented for comprehensive error analysis in the solutions of the Caputo fractional Rössler attractor model,depicting each computation in graphs and tables to analyze how fractional order affects the model’s dynamics.Approximate solutions obtained through the proposed scheme for integer order are well comparable with the fourth-order Runge-Kutta method.Also,the stability analyses of the considered model are discussed for different equilibrium points.Various fractional orders are considered while performing numerical simulations for the Caputo fractional Rössler attractor model by using Mathematica.The suggested approach can solve another non-linear fractional model due to its straightforward implementation.展开更多
This paper presents the problem of generating four-wing （eight-wing） chaotic attractors. The adopted method consists in suitably coupling two （three） identical Lorenz systems. In analogy with the original Lorenz s...This paper presents the problem of generating four-wing （eight-wing） chaotic attractors. The adopted method consists in suitably coupling two （three） identical Lorenz systems. In analogy with the original Lorenz system, where the two wings of the butterfly attractor are located around the two equilibria with the unstable pair of complex-conjugate eigenvalues, this paper shows that the four wings （eight wings） of these novel attractors axe located around the four （eight） equilibria with two （three） pairs of unstable complex-conjugate eigenvalues.展开更多
In this paper, we consider a reaction diffusion system with Hamitonian structure, we first prove the existence of an invariant region for system and the continuity of the semigroup, then establish the absorbing sets ...In this paper, we consider a reaction diffusion system with Hamitonian structure, we first prove the existence of an invariant region for system and the continuity of the semigroup, then establish the absorbing sets and global attractor.展开更多
In this paper,we propose an innovative chaotic system,combining fractional derivative and sinehyperbolic nonlinearity with circuit execution.The study of this system is conducted via an analog circuit simulator,using ...In this paper,we propose an innovative chaotic system,combining fractional derivative and sinehyperbolic nonlinearity with circuit execution.The study of this system is conducted via an analog circuit simulator,using two anti-parallel semiconductor diodes to provide hyperbolic sine nonlinearity,and to function as operational amplifiers.The multi-stability of the system is also enhanced with the help of multi-equilibrium points for distinct real orders of system.The system explores the generation of a four-wing attractor in different phases,both numerically and electronically.By changing the input parameters of the system,different graphs are generated for current flow in state,phase,and space,to confirm the precision of the fractional order derivatives.A reasonable simulation shows that the deliberate circuit provides effective chaos in terms of speed and accuracy,which is comensurate with the numerical simulation.This nonlinear chaotic behavior is utilized to encrypt sound(.wav),images(.jpg),and animated(.gif)data which are a major requirement for the security of communication systems.The proposed circuit performs chaos and cryptographic tasks with high-effective analog computation,and constitutes a novel approach to this area of research.展开更多
This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms,and the system can generate a single four-wing chaotic attractor with wide...This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms,and the system can generate a single four-wing chaotic attractor with wide parameter ranges. Through theoretical analysis,the Hopf bifurcation processes are proved to arise at certain equilibrium points.Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours;the system trajectory can evolve to a chaotic attractor from a periodic orbit or a fixed point as the proper parameter varies. Finally,an analog electronic circuit is designed to physically realize the chaotic system;the existence of four-wing chaotic attractor is verified by the analog circuit realization.展开更多
The initial-boundary value problem of the propagation of nonlinear longitudinal elastic waves in an initially strained rod is considered. The rod is assumed to interact with the surrouding elastic and viscous external...The initial-boundary value problem of the propagation of nonlinear longitudinal elastic waves in an initially strained rod is considered. The rod is assumed to interact with the surrouding elastic and viscous external medium. The long time behavior of solutions are derived and global attractors in E-1 space is obtained.展开更多
In this paper, we propose a novel four-dimensional autonomous chaotic system. Of particular interest is that this novel system can generate one-, two, three- and four-wing chaotic attractors with the variation of a si...In this paper, we propose a novel four-dimensional autonomous chaotic system. Of particular interest is that this novel system can generate one-, two, three- and four-wing chaotic attractors with the variation of a single parameter, and the multi-wing type of the chaotic attractors can be displayed in all directions. The system is simple with a large positive Lyapunov exponent and can exhibit some interesting and complicated dynamical behaviours. Basic dynamical properties of the four-dimensional chaotic system, such as equilibrium points, the Poincare map, the bifurcation diagram and the Lyapunov exponents are investigated by using either theoretical analysis or numerical method. Finally, a circuit is designed for the implementation of the multi-wing chaotic attractors. The electronic workbench observations axe in good agreement with the numerical simulation results.展开更多
In this article, we consider the existence of trajectory and global attractors for nonclassical diffusion equations with linear fading memory. For this purpose, we will apply the method presented by Chepyzhov and Mira...In this article, we consider the existence of trajectory and global attractors for nonclassical diffusion equations with linear fading memory. For this purpose, we will apply the method presented by Chepyzhov and Miranville [7, 8], in which the authors provide some new ideas in describing the trajectory attractors for evolution equations with memory.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 62366014 and 61961019)the Natural Science Foundation of Jiangxi Province, China (Grant No. 20232BAB202008)。
文摘This article proposes a non-ideal flux-controlled memristor with a bisymmetric sawtooth piecewise function, and a new multi-wing memristive chaotic system(MMCS) based on the memristor is generated. Compared with other existing MMCSs, the most eye-catching point of the proposed MMCS is that the amplitude of the wing will enlarge towards the poles as the number of wings increases. Diverse coexisting attractors are numerically found in the MMCS, including chaos,quasi-period, and stable point. The circuits of the proposed memristor and MMCS are designed and the obtained results demonstrate their validity and reliability.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51177117 and 51307130)
文摘A novel 5-dimensional（5D） memristive chaotic system is proposed, in which multi-scroll hidden attractors and multiwing hidden attractors can be observed on different phase planes. The dynamical system has multiple lines of equilibria or no equilibrium when the system parameters are appropriately selected, and the multi-scroll hidden attractors and multi-wing hidden attractors have nothing to do with the system equilibria. Particularly, the numbers of multi-scroll hidden attractors and multi-wing hidden attractors are sensitive to the transient simulation time and the initial values. Dynamical properties of the system, such as phase plane, time series, frequency spectra, Lyapunov exponent, and Poincar′e map, are studied in detail. In addition, a state feedback controller is designed to select multiple hidden attractors within a long enough simulation time. Finally, an electronic circuit is realized in Pspice, and the experimental results are in agreement with the numerical ones.
基金Project supported by the National Natural Science Foundation of China(Grant No.61403143)the Natural Science Foundation of Guangdong Province,China(Grant No.2014A030313739)+1 种基金the Science and Technology Foundation Program of Guangzhou City,China(Grant No.201510010124)the Excellent Doctorial Dissertation Foundation of Guangdong Province,China(Grant No.XM080054)
文摘This paper aims at developing a novel method of constructing a class of multi-wing chaotic and hyperchaotic system by introducing a unified step function. In order to overcome the essential difficulties in iteratively adjusting multiple parameters of conventional multi-parameter control, this paper introduces a unified step function controlled by a single parameter for constructing various multi-wing chaotic and hyperchaotic systems. In particular, to the best of the authors＇ knowledge, this is also the first time to find a non-equilibrium multi-wing hyperchaotic system by means of the unified step function control. According to the heteroclinic loop Shilnikov theorem, some properties for multi-wing attractors and its chaos mechanism are further discussed and analyzed. A circuit for multi-wing systems is designed and implemented for demonstration, which verifies the effectiveness of the proposed approach.
基金supported by the National Natural Science Foundation of China(Grant No.U20A20110)the Second Tibetan Plateau Scientific Expedition and Research Program(Grant No.2019QZKK0906)+2 种基金the Key R&D Projects of Tibet Autonomous Region Science and Technology Pro ject(Grant No.XZ202101ZD0013G)the International Cooperation Overseas Platform Project,CAS(Grant No.131C11KYSB20200033)the Outstanding Talent Project of Thousand Talents Program in China.
文摘The catastrophic rockslide,which frequently triggers numerous severe disasters worldwide,has drawn much attention globally;however,understanding the initiation mechanism of catastrophic rockslides in the absence of typical single triggering factors related to strong seismic activity or torrential precipitation continues to be challenging within the global scientific community.This study aims to determine the mechanism of the three largest catastrophic rockslides in the eastern Tibetan Plateau,Yigong,Xinmo,and Baige,over the past 20 years using field investigation,remote sensing,and runoff analysis.Instead of the conventional driving factors of heavy rainfall and strong earthquakes,the multi-wing butterfly effects(MWBE)of climatic factors and weak earthquakes are for the first time identified as drivers of the catastrophic rockslide disasters.First,strong tectonic uplift,fast fluvial incision,high-density faults,and large regional water confluence formed the slopes in the critical regime,creating the source conditions of rockslide.Second,the MWBE of early dry-heat events and antecedent rainfall,combined with imminent weak earthquakes,initiated rockslide.Third,the delayed amplified runoff moving toward the sliding surface and lowering the strength of the locking-rock segment constituted the fundamental mechanism of the MWBE on rockslide.The catastrophic rockslide was ultimately inferred to be a nonlinear chaotic process;however,prediction and forecasting of rockslide based on the MWBE in the early stages are possible and essential.This finding presents a new perspective concerning forecasting progressive landslides.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61161006 and 61073187)
文摘The complexities of multi-wing chaotic systems based on the modified Chen system and a multi-segment quadratic function are investigated by employing the statistical complexity measure （SCM） and the spectral entropy （SE） algorithm. How to choose the parameters of the SCM and SE algorithms is discussed. The results show that the complexity of the multi-wing chaotic system does not increase as the number of wings increases, and it is consistent with the results of the Grassberger-Procaccia （GP） algorithm and the largest Lyapunov exponent （LLE） of the multi-wing chaotic system.
基金supported by the National Natural Science Foundation of China(Grant No.12475008)the Scientific Research and Developed Fund of Zhejiang A&F University(Grant No.2021FR0009)。
文摘This study systematically investigates the attractor characteristics of harmonic solitons in a passively modelocked fiber laser.Through comprehensive analysis in both time and frequency domains,we examine the evolution of pulse width,spectral bandwidth,and energy across different harmonic orders.The results demonstrate typical soliton attractor behaviors,including attractiveness,dissipativity,and self-organization.In the transition regions between harmonic orders,breathing harmonic soliton states are captured using the time-stretched dispersive Fourier transform.By comparing the breathing dynamics with the stable states,the existence and self-organizing nature of soliton attractors are further confirmed.Finally,harmonic soliton attractors are employed as programmable light sources to achieve ternary optical coding.
基金supported by the NSFC(12271141)supported by the Fundamental Research Funds for the Central Universities(B240205026)the Postgraduate Research and Practice Innovation Program of Jiangsu Province(KYCX24_0821).
文摘In this paper, we consider the existence of pullback random exponential attractor for non-autonomous random reaction-diffusion equation driven by nonlinear colored noise defined onR^(N) . The key steps of the proof are the tails estimate and to demonstrate the Lipschitz continuity and random squeezing property of the solution for the equation defined on R^(N) .
基金Supported by the National Natural Science Foundation of China(11971378)Shaanxi Fundamental Science Research Project for Mathematics and Physics(23JSY050)Shaanxi Innovative Training Program for College Students(S202410719114)。
文摘In this article,the global attractors of 2D g-Navier-Stokes equations are obtained in the space of C_(Hg) and CVg respectively.When the external force f is sufficiently small,the studies indicate that the global attractor in C_(Hg) is equal to the global attractor in C_(Vg).
基金Project supported by the Basic Scientific Research Projects of Department of Education of Liaoning Province,China(Grant No.LJ212410152049)the Technological Innovation Projects in the field of artificial intelligence of Liaoning Province,China(Grant No.2023JH26/10300011)。
文摘Existing chaotic encryption schemes primarily focus on single types of images,making the design of hybrid image encryption schemes more suitable for practical applications.In this paper,a hyperchaotic map with a spherical attractor is proposed,which is constructed using spherical coordinates.Dynamical analyses reveal that the hyperchaotic map exhibits global hyperchaos and high complexity,making it capable of generating more complex chaotic sequences suitable for image encryption.A hybrid encryption scheme based on a hyperchaotic map is proposed for two-dimensional(2D)images,three-dimensional(3D)models,and 3D point clouds.Firstly,the pixels of 2D image and the coordinate data of 3D image are fused into a plaintext cube,which is combined with Hash-512 to obtain the initial value of the hyperchaotic map.Chaotic sequences are utilized for cube space internal confusion and dynamic cross-diffusion.The encrypted images demonstrate high information entropy,and the test results show that the encryption scheme effectively protects the images.The proposed hybrid image encryption scheme provides an efficient solution for securing various types of images.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1210150211961059)the University Innovation Project of Gansu Province(Grant No.2023B-062).
文摘The paper is devoted to establishing the long-time behavior of solutions to the extensible beam equation with rotational inertia and nonlocal strong damping.Within the theory of asymptotical smoothness,we investigate the existence of the attractor by using the contractive function method and more detailed estimates.
基金supported by the National Natural Science Foundation of China(Grant No.62001391)the Guangdong Basic and Applied Basic Research Foundation(Grant No.2024A1515010308)+1 种基金the Natural Science Basic Research Program of Shaanxi(Grant No.2024JC-YBQN-0464)the Scientific Research Program Funded by Education Department of Shaanxi Provincial Government(Grant No.24JK0559).
文摘This paper proposes a universal impulse-function-based method for extending discrete chaotic maps,enabling flexible construction of multicavity chaotic attractors.The proposed method achieves one-directional(1D)/two-directional(2D)extensions without introducing additional nonlinear terms or altering system stability.Theoretically,the cavity quantity in arbitrary directions is controlled by adjusting impulse levels N,while the amplitude regulation is implemented through modifications to the proportionality parameter r.Theoretical analyses,including Lyapunov exponents(LEs)and bifurcation diagrams,are conducted,confirming that the extended maps retain the intrinsic dynamics of five rational map classes.The field-programmable gate array(FPGA)implementation results are consistent with the numerical simulation results,verifying the correctness of the theoretical analysis.The method enables the expansion of unipolar attractors and enhances entropy metrics,offering a robust framework for applications in secure communication,encryption,and chaos-based technologies.
基金"La derivada fraccional generalizada,nuevos resultados y aplicaciones a desigualdades integrales"Cod UIO-077-2024supported via funding from Prince Sattam bin Abdulaziz University project number(PSAU/2025/R/1446).
文摘The Rössler attractor model is an important model that provides valuable insights into the behavior of chaotic systems in real life and is applicable in understanding weather patterns,biological systems,and secure communications.So,this work aims to present the numerical performances of the nonlinear fractional Rössler attractor system under Caputo derivatives by designing the numerical framework based on Ultraspherical wavelets.The Caputo fractional Rössler attractor model is simulated into two categories,(i)Asymmetric and(ii)Symmetric.The Ultraspherical wavelets basis with suitable collocation grids is implemented for comprehensive error analysis in the solutions of the Caputo fractional Rössler attractor model,depicting each computation in graphs and tables to analyze how fractional order affects the model’s dynamics.Approximate solutions obtained through the proposed scheme for integer order are well comparable with the fourth-order Runge-Kutta method.Also,the stability analyses of the considered model are discussed for different equilibrium points.Various fractional orders are considered while performing numerical simulations for the Caputo fractional Rössler attractor model by using Mathematica.The suggested approach can solve another non-linear fractional model due to its straightforward implementation.
文摘This paper presents the problem of generating four-wing （eight-wing） chaotic attractors. The adopted method consists in suitably coupling two （three） identical Lorenz systems. In analogy with the original Lorenz system, where the two wings of the butterfly attractor are located around the two equilibria with the unstable pair of complex-conjugate eigenvalues, this paper shows that the four wings （eight wings） of these novel attractors axe located around the four （eight） equilibria with two （three） pairs of unstable complex-conjugate eigenvalues.
文摘In this paper, we consider a reaction diffusion system with Hamitonian structure, we first prove the existence of an invariant region for system and the continuity of the semigroup, then establish the absorbing sets and global attractor.
文摘In this paper,we propose an innovative chaotic system,combining fractional derivative and sinehyperbolic nonlinearity with circuit execution.The study of this system is conducted via an analog circuit simulator,using two anti-parallel semiconductor diodes to provide hyperbolic sine nonlinearity,and to function as operational amplifiers.The multi-stability of the system is also enhanced with the help of multi-equilibrium points for distinct real orders of system.The system explores the generation of a four-wing attractor in different phases,both numerically and electronically.By changing the input parameters of the system,different graphs are generated for current flow in state,phase,and space,to confirm the precision of the fractional order derivatives.A reasonable simulation shows that the deliberate circuit provides effective chaos in terms of speed and accuracy,which is comensurate with the numerical simulation.This nonlinear chaotic behavior is utilized to encrypt sound(.wav),images(.jpg),and animated(.gif)data which are a major requirement for the security of communication systems.The proposed circuit performs chaos and cryptographic tasks with high-effective analog computation,and constitutes a novel approach to this area of research.
基金Project supported by the National Natural Science Foundation of China(Grant Nos 60774088 and 10772135)the Foundation of the Application Base and Frontier Technology Research Project of Tianjin,China (Grant Nos 07JCZDJC09600,08JCZDJC21900 and 08JCZDJC18600)the Tianjin Key Laboratory for Control Theory & Applications in Complicated Industry Systems of China
文摘This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms,and the system can generate a single four-wing chaotic attractor with wide parameter ranges. Through theoretical analysis,the Hopf bifurcation processes are proved to arise at certain equilibrium points.Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours;the system trajectory can evolve to a chaotic attractor from a periodic orbit or a fixed point as the proper parameter varies. Finally,an analog electronic circuit is designed to physically realize the chaotic system;the existence of four-wing chaotic attractor is verified by the analog circuit realization.
基金National Natural Science Foundation of China!(No:19861004)
文摘The initial-boundary value problem of the propagation of nonlinear longitudinal elastic waves in an initially strained rod is considered. The rod is assumed to interact with the surrouding elastic and viscous external medium. The long time behavior of solutions are derived and global attractors in E-1 space is obtained.
文摘In this paper, we propose a novel four-dimensional autonomous chaotic system. Of particular interest is that this novel system can generate one-, two, three- and four-wing chaotic attractors with the variation of a single parameter, and the multi-wing type of the chaotic attractors can be displayed in all directions. The system is simple with a large positive Lyapunov exponent and can exhibit some interesting and complicated dynamical behaviours. Basic dynamical properties of the four-dimensional chaotic system, such as equilibrium points, the Poincare map, the bifurcation diagram and the Lyapunov exponents are investigated by using either theoretical analysis or numerical method. Finally, a circuit is designed for the implementation of the multi-wing chaotic attractors. The electronic workbench observations axe in good agreement with the numerical simulation results.
基金supported by NSFC Grant (11031003)the Fundamental Research Funds for the Central Universities+1 种基金support by Fund of excellent young teachers in Shanghai (shgcjs008)Initial Fund of SUES (A-0501-11-016)
文摘In this article, we consider the existence of trajectory and global attractors for nonclassical diffusion equations with linear fading memory. For this purpose, we will apply the method presented by Chepyzhov and Miranville [7, 8], in which the authors provide some new ideas in describing the trajectory attractors for evolution equations with memory.
