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
This paper proposes a novel approach for generating a multi-scroll chaotic system. Together with the theoretical design and numerical simulations, three different types of attractor are available, governed by construc...This paper proposes a novel approach for generating a multi-scroll chaotic system. Together with the theoretical design and numerical simulations, three different types of attractor are available, governed by constructing triangular wave, sawtooth wave and hysteresis sequence. The presented new multi-scroll chaotic system is different from the classical multi-scroll chaotic Chua system in dimensionless state equations, nonlinear functions and maximum Lyapunov exponents. In addition, the basic dynamical behaviours, including equilibrium points, eigenvalues, eigenvectors, eigenplanes, bifurcation diagrams and Lyapunov exponents, are further investigated. The success of the design is illustrated by both numerical simulations and circuit experiments.展开更多
In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness o...In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness of the solution by priori estimation and the Galerkin method. Then, we obtain to the existence of the global attractor. At last, we consider that the estimation of the upper bounds of Hausdorff and fractal dimensions for the global attractors are obtained.展开更多
We investigate the global well-posedness and the global attractors of the solutions for the Higher-order Kirchhoff-type wave equation with nonlinear strongly damping: . For strong nonlinear damping σ and ?, we make a...We investigate the global well-posedness and the global attractors of the solutions for the Higher-order Kirchhoff-type wave equation with nonlinear strongly damping: . For strong nonlinear damping σ and ?, we make assumptions (H<sub>1</sub>) - (H<sub>4</sub>). Under of the proper assume, the main results are existence and uniqueness of the solution in proved by Galerkin method, and deal with the global attractors.展开更多
The pollen donor and pollinator attractor hypotheses are explanations for the functions of the male flowers of andromonoecious plants. We tested these two hypotheses in the andromonoecious shrub Capparis spinosa L. （...The pollen donor and pollinator attractor hypotheses are explanations for the functions of the male flowers of andromonoecious plants. We tested these two hypotheses in the andromonoecious shrub Capparis spinosa L. （Capparaceae） and confirmed that pollen production and cumulative volume and sugar concentration of nectar do not differ between male and perfect flowers. However, male flowers produced larger anthers, larger pollen grains and smaller ovaries than perfect flowers. Observations on pollinators indicated that two major pollinators （Xylocopa valga Gerst and Proxylocopa sinensis Wu） did not discriminate between flower morphs and that they transferred pollen grains a similar distance. However, there were more seeds per fruit following hand pollination with pollen from male flowers than from perfect flowers. Individuals of C. spinosa with a larger floral display （i.e. bearing more flowers） received more pollen grains on the stigma of perfect flowers. Female reproductive success probably is not limited by pollen. These results indicate that male flowers of C. spinosa save resources for female function and that they primarily serve to attract pollinators as pollen donors.展开更多
Coexistence of attractors with striking characteristics is observed in this work, where a stable period-5 attractor coexists successively with chaotic band-ll, period-6, chaotic band-12 and band-6 attractors. They are...Coexistence of attractors with striking characteristics is observed in this work, where a stable period-5 attractor coexists successively with chaotic band-ll, period-6, chaotic band-12 and band-6 attractors. They are induced by dif- ferent mechanisms due to the interaction between the discontinuity and the non-invertibility. A characteristic boundary collision bifurcation, is observed. The critical conditions are obtained both analytically and numerically.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
In this paper, we studied a family of the exponential attractors and the inertial manifolds for a class of generalized Kirchhoff-type equations with strong dissipation term. After making appropriate assumptions for Ki...In this paper, we studied a family of the exponential attractors and the inertial manifolds for a class of generalized Kirchhoff-type equations with strong dissipation term. After making appropriate assumptions for Kirchhoff stress term and nonlinear term, the existence of exponential attractor is obtained by proving the discrete squeezing property of the equation, then according to Hadamard’s graph transformation method, the spectral interval condition is proved to be true, therefore, the existence of a family of the inertial manifolds for the equation is obtained.展开更多
This article examines the dynamics for stochastic plate equations with linear memory in the case of bounded domain. We investigate the existence of solutions and bounded absorbing set by using the uniform pullback att...This article examines the dynamics for stochastic plate equations with linear memory in the case of bounded domain. We investigate the existence of solutions and bounded absorbing set by using the uniform pullback attractors on the tails estimates, and the asymptotic compactness of the random dynamical system is proved by decomposition method, and then we obtain the existence of a random attractor.展开更多
In this paper, we consider the weakly damped wave equations with hereditary effects, and the nonlinearity f satisfies critical growth. The delay term g（t, ut） may be driven by a function with very weak assumptions, ...In this paper, we consider the weakly damped wave equations with hereditary effects, and the nonlinearity f satisfies critical growth. The delay term g（t, ut） may be driven by a function with very weak assumptions, namely, just measurability. We analyze the well-posedness of solutions and verify the existence of the pullback ：D-attractor in CH01（Ω） × CL2 （Ω） by constructing the energy functional and combining with the idea of the contractive function.展开更多
In this paper, we investigate the existence of random attractor for the random dynamical system generated by the Kirchhoff-type suspension bridge equations with strong damping and white noises. We first prove the exis...In this paper, we investigate the existence of random attractor for the random dynamical system generated by the Kirchhoff-type suspension bridge equations with strong damping and white noises. We first prove the existence and uniqueness of solutions to the initial boundary value conditions, and then we study the existence of the global attractors of the equation.展开更多
In this paper, we prove the existence of random attractors for a stochastic reaction-diffusion equation with distribution derivatives on unbounded domains. The nonlinearity is dissipative for large values of the state...In this paper, we prove the existence of random attractors for a stochastic reaction-diffusion equation with distribution derivatives on unbounded domains. The nonlinearity is dissipative for large values of the state and the stochastic nature of the equation appears spatially distributed temporal white noise. The stochastic reaction-diffusion equation is recast as a continuous random dynamical system and asymptotic compactness for this demonstrated by using uniform estimates far-field values of solutions. The results are new and appear to be optimal.展开更多
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.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 60572073 and 60871025)the Natural Science Foundation of Guangdong Province,China (Grant Nos 8151009001000060,5001818 and 8351009001000002)
文摘This paper proposes a novel approach for generating a multi-scroll chaotic system. Together with the theoretical design and numerical simulations, three different types of attractor are available, governed by constructing triangular wave, sawtooth wave and hysteresis sequence. The presented new multi-scroll chaotic system is different from the classical multi-scroll chaotic Chua system in dimensionless state equations, nonlinear functions and maximum Lyapunov exponents. In addition, the basic dynamical behaviours, including equilibrium points, eigenvalues, eigenvectors, eigenplanes, bifurcation diagrams and Lyapunov exponents, are further investigated. The success of the design is illustrated by both numerical simulations and circuit experiments.
文摘In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness of the solution by priori estimation and the Galerkin method. Then, we obtain to the existence of the global attractor. At last, we consider that the estimation of the upper bounds of Hausdorff and fractal dimensions for the global attractors are obtained.
文摘We investigate the global well-posedness and the global attractors of the solutions for the Higher-order Kirchhoff-type wave equation with nonlinear strongly damping: . For strong nonlinear damping σ and ?, we make assumptions (H<sub>1</sub>) - (H<sub>4</sub>). Under of the proper assume, the main results are existence and uniqueness of the solution in proved by Galerkin method, and deal with the global attractors.
基金Supported by the Projects on the Research and Development of High Technology of Xinjiang Uygur Autonomous Region (200810102), China, the Construction of Scientific and Technological Platforms Project from the Chinese Ministry of Science and Technology (2005DKA21006 and 2005DKA21403)the National Natural Science Foundation of China (90302004).
文摘The pollen donor and pollinator attractor hypotheses are explanations for the functions of the male flowers of andromonoecious plants. We tested these two hypotheses in the andromonoecious shrub Capparis spinosa L. （Capparaceae） and confirmed that pollen production and cumulative volume and sugar concentration of nectar do not differ between male and perfect flowers. However, male flowers produced larger anthers, larger pollen grains and smaller ovaries than perfect flowers. Observations on pollinators indicated that two major pollinators （Xylocopa valga Gerst and Proxylocopa sinensis Wu） did not discriminate between flower morphs and that they transferred pollen grains a similar distance. However, there were more seeds per fruit following hand pollination with pollen from male flowers than from perfect flowers. Individuals of C. spinosa with a larger floral display （i.e. bearing more flowers） received more pollen grains on the stigma of perfect flowers. Female reproductive success probably is not limited by pollen. These results indicate that male flowers of C. spinosa save resources for female function and that they primarily serve to attract pollinators as pollen donors.
基金Project supported by the National Natural Science Foundation of China (Grant No 10275053)
文摘Coexistence of attractors with striking characteristics is observed in this work, where a stable period-5 attractor coexists successively with chaotic band-ll, period-6, chaotic band-12 and band-6 attractors. They are induced by dif- ferent mechanisms due to the interaction between the discontinuity and the non-invertibility. A characteristic boundary collision bifurcation, is observed. The critical conditions are obtained both analytically and numerically.
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.
文摘In this paper, we studied a family of the exponential attractors and the inertial manifolds for a class of generalized Kirchhoff-type equations with strong dissipation term. After making appropriate assumptions for Kirchhoff stress term and nonlinear term, the existence of exponential attractor is obtained by proving the discrete squeezing property of the equation, then according to Hadamard’s graph transformation method, the spectral interval condition is proved to be true, therefore, the existence of a family of the inertial manifolds for the equation is obtained.
文摘This article examines the dynamics for stochastic plate equations with linear memory in the case of bounded domain. We investigate the existence of solutions and bounded absorbing set by using the uniform pullback attractors on the tails estimates, and the asymptotic compactness of the random dynamical system is proved by decomposition method, and then we obtain the existence of a random attractor.
基金Supported by the NSFC(Grants Nos.11471148 and 11601522)the Fundamental Research Funds for the Central Universities of China(Grant No.17CX02036A)the Provincial Natural Science Foundation of Hu’nan(Grant No.2017JJ3222)
文摘In this paper, we consider the weakly damped wave equations with hereditary effects, and the nonlinearity f satisfies critical growth. The delay term g（t, ut） may be driven by a function with very weak assumptions, namely, just measurability. We analyze the well-posedness of solutions and verify the existence of the pullback ：D-attractor in CH01（Ω） × CL2 （Ω） by constructing the energy functional and combining with the idea of the contractive function.
文摘In this paper, we investigate the existence of random attractor for the random dynamical system generated by the Kirchhoff-type suspension bridge equations with strong damping and white noises. We first prove the existence and uniqueness of solutions to the initial boundary value conditions, and then we study the existence of the global attractors of the equation.
文摘In this paper, we prove the existence of random attractors for a stochastic reaction-diffusion equation with distribution derivatives on unbounded domains. The nonlinearity is dissipative for large values of the state and the stochastic nature of the equation appears spatially distributed temporal white noise. The stochastic reaction-diffusion equation is recast as a continuous random dynamical system and asymptotic compactness for this demonstrated by using uniform estimates far-field values of solutions. The results are new and appear to be optimal.
