The existence of a global attractor is established for generalized Navier-Stokes equations incorporating damping term within the periodic domainΩ=[−π,π]^(n).Initially,we show the existence and uniqueness of strong ...The existence of a global attractor is established for generalized Navier-Stokes equations incorporating damping term within the periodic domainΩ=[−π,π]^(n).Initially,we show the existence and uniqueness of strong solutions.Subsequently,we verify the continuity of the associated semigroup when max{2n+1/n-1,5n+2/3n-2} < β <3n+2/n-2.Finally,we establish the existence of both H^(α)-global attractor and H^(2α)-global attractor.展开更多
The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and e...The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and existence of uniform attractor under some suitable assumptions on the nonlinear term g(u),the nonlinear damping f(u_(t))and the external force h(x,t).Specifically,the asymptotic compactness of the semigroup is verified by the energy reconstruction method.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
This paper investigates global solutions and long-time dynamics for the stochastic reaction-diffusion equation du=(Δu+f(u)+g(x,t))dt+σ(u)dW on a bounded domain,where the drift term f(u),with polynomial growth rate ...This paper investigates global solutions and long-time dynamics for the stochastic reaction-diffusion equation du=(Δu+f(u)+g(x,t))dt+σ(u)dW on a bounded domain,where the drift term f(u),with polynomial growth rate β,is strongly dissipative and the diffusion term σ(u)has growth rate γ,satisfying β+1>2γ.Under this condition,we establish the existence,uniqueness,and regularity of solutions in Bochner spaces.Our analysis relies only on weak monotonicity conditions and requires no further growth restrictions on f andσ.Moreover,we prove the existence of a weak mean random attractor for the system.These results offer new insights into the balance mechanism between stochastic perturbations and dissipative effects in superlinear regimes.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
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
Due to uncertain push-pull action across boundaries between different attractive domains by random excitations, attractors of a dynamical system will drift in the phase space, which readily leads to colliding and mixi...Due to uncertain push-pull action across boundaries between different attractive domains by random excitations, attractors of a dynamical system will drift in the phase space, which readily leads to colliding and mixing with each other, so it is very difficult to identify irregular signals evolving from arbitrary initial states. Here, periodic attractors from the simple cell mapping method are further iterated by a specific Poincare map in order to observe more elaborate structures and drifts as well as possible dynamical bifurcations. The panorama of a chaotic attractor can also be displayed to a great extent by this newly developed procedure. From the positions and the variations of attractors in the phase space, the action mechanism of bounded noise excitation is studied in detail. Several numerical examples are employed to illustrate the present procedure. It is seen that the dynamical identification and the bifurcation analysis can be effectively performed by this procedure.展开更多
The long time behavior of solution for Hirota equation with zero order dissipation is studied. The global weak attractor for this system in Hper^k is constructed. And then by exact analysis of the energy equation, it ...The long time behavior of solution for Hirota equation with zero order dissipation is studied. The global weak attractor for this system in Hper^k is constructed. And then by exact analysis of the energy equation, it is shown that the global weak attractor is actually the global strong attractor in Hper^k.展开更多
A class of strongly damped nonlinear wave equations are studied by using the technique of the operator decomposition,and the existence of the global compact attractor in space D(A)×V is obtained.
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
文摘The existence of a global attractor is established for generalized Navier-Stokes equations incorporating damping term within the periodic domainΩ=[−π,π]^(n).Initially,we show the existence and uniqueness of strong solutions.Subsequently,we verify the continuity of the associated semigroup when max{2n+1/n-1,5n+2/3n-2} < β <3n+2/n-2.Finally,we establish the existence of both H^(α)-global attractor and H^(2α)-global attractor.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11961059,1210502)the University Innovation Project of Gansu Province(Grant No.2023B-062)the Gansu Province Basic Research Innovation Group Project(Grant No.23JRRA684).
文摘The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and existence of uniform attractor under some suitable assumptions on the nonlinear term g(u),the nonlinear damping f(u_(t))and the external force h(x,t).Specifically,the asymptotic compactness of the semigroup is verified by the energy reconstruction method.
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(No.12271399)the Fundamental Research Funds for the Central Universities(No.3122025090)。
文摘This paper investigates global solutions and long-time dynamics for the stochastic reaction-diffusion equation du=(Δu+f(u)+g(x,t))dt+σ(u)dW on a bounded domain,where the drift term f(u),with polynomial growth rate β,is strongly dissipative and the diffusion term σ(u)has growth rate γ,satisfying β+1>2γ.Under this condition,we establish the existence,uniqueness,and regularity of solutions in Bochner spaces.Our analysis relies only on weak monotonicity conditions and requires no further growth restrictions on f andσ.Moreover,we prove the existence of a weak mean random attractor for the system.These results offer new insights into the balance mechanism between stochastic perturbations and dissipative effects in superlinear regimes.
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.
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supported by the National Natural Science Foundation of China (10672140,11072213)
文摘Due to uncertain push-pull action across boundaries between different attractive domains by random excitations, attractors of a dynamical system will drift in the phase space, which readily leads to colliding and mixing with each other, so it is very difficult to identify irregular signals evolving from arbitrary initial states. Here, periodic attractors from the simple cell mapping method are further iterated by a specific Poincare map in order to observe more elaborate structures and drifts as well as possible dynamical bifurcations. The panorama of a chaotic attractor can also be displayed to a great extent by this newly developed procedure. From the positions and the variations of attractors in the phase space, the action mechanism of bounded noise excitation is studied in detail. Several numerical examples are employed to illustrate the present procedure. It is seen that the dynamical identification and the bifurcation analysis can be effectively performed by this procedure.
基金Supported by the Natural science Foundation of Henan Education Department(2007110004)the Natural Science Foundation of Henan University(06YBZR027)
文摘The long time behavior of solution for Hirota equation with zero order dissipation is studied. The global weak attractor for this system in Hper^k is constructed. And then by exact analysis of the energy equation, it is shown that the global weak attractor is actually the global strong attractor in Hper^k.
文摘A class of strongly damped nonlinear wave equations are studied by using the technique of the operator decomposition,and the existence of the global compact attractor in space D(A)×V is obtained.
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.
