为设计性能较好的伪随机数发生器,提出了一个满足修正的马罗驼(Marotto)定理的新二维离散混沌系统(2DCS)。利用离散广义混沌同步理论和2D-CS构造了一个广义同步混沌系统(2D-GCS);通过一个实数域到整数域的变换设计了一个混沌伪随机数生...为设计性能较好的伪随机数发生器,提出了一个满足修正的马罗驼(Marotto)定理的新二维离散混沌系统(2DCS)。利用离散广义混沌同步理论和2D-CS构造了一个广义同步混沌系统(2D-GCS);通过一个实数域到整数域的变换设计了一个混沌伪随机数生成器(CPRNG);利用美国联邦信息处理标准(federal information processing standards,FIPS)提出的FIPS 140-2检测包分别对CPRNG和RC4算法产生的1000个二进制序列的随机性进行检测,结果均通过了检测。检测结果的平均值和方差对比表明CPRNG和RC4算法产生的伪随机序列随机性能相当,相关性检测结果表明该CPRNG在不同的密钥扰动下产生的密钥各组序列几乎完全独立,设计的CPRNG能产生性能良好的伪随机数。展开更多
In this paper, an approach for chaotifying a stable controllable linear system via single input state-feedback is presented. The overflow function of the system states is designed as the feedback controller, which can...In this paper, an approach for chaotifying a stable controllable linear system via single input state-feedback is presented. The overflow function of the system states is designed as the feedback controller, which can make the fixed point of the closed-loop system to be a snap-back repeller, thereby yields chaotic dynamics. Based on the Marotto theorem, it proves theoretically that the closed-loop system is chaotic in the sense of Li and Yorke. Finally, the simulation results are used to illustrate the effectiveness of the proposed method.展开更多
In this paper, we investigate the complex dynamics of two-species Ricker-type discrete-time competitive model. We perform a local stability analysis for the fixed points and we will discuss about its persistence for b...In this paper, we investigate the complex dynamics of two-species Ricker-type discrete-time competitive model. We perform a local stability analysis for the fixed points and we will discuss about its persistence for boundary fixed points. This system inherits the dynamics of one-dimensional Ricker model such as cascade of period-doubling bifurcation, periodic windows and chaos. We explore the existence of chaos for the equilibrium points for a specific case of this system using Marotto theorem and proving the existence of snap-back repeller. We use several dynamical systems tools to demonstrate the qualitative behaviors of the system.展开更多
This paper is concerned with chaos in discrete dynamical systems governed by continuously Frechet differentiable maps in Banach spaces. A criterion of chaos induced by a regular nondegenerate homoclinic orbit is estab...This paper is concerned with chaos in discrete dynamical systems governed by continuously Frechet differentiable maps in Banach spaces. A criterion of chaos induced by a regular nondegenerate homoclinic orbit is established. Chaos of discrete dynamical systems in the n-dimensional real space is also discussed, with two criteria derived for chaos induced by nondegenerate snap-back repellers, one of which is a modified version of Marotto's theorem. In particular, a necessary and sufficient condition is obtained for an expanding fixed point of a differentiable map in a general Banach space and in an n-dimensional real space, respectively. It completely solves a long-standing puzzle about the relationship between the expansion of a continuously differentiable map near a fixed point in an n-dimensional real space and the eigenvalues of the Jacobi matrix of the map at the fixed point.展开更多
文摘为设计性能较好的伪随机数发生器,提出了一个满足修正的马罗驼(Marotto)定理的新二维离散混沌系统(2DCS)。利用离散广义混沌同步理论和2D-CS构造了一个广义同步混沌系统(2D-GCS);通过一个实数域到整数域的变换设计了一个混沌伪随机数生成器(CPRNG);利用美国联邦信息处理标准(federal information processing standards,FIPS)提出的FIPS 140-2检测包分别对CPRNG和RC4算法产生的1000个二进制序列的随机性进行检测,结果均通过了检测。检测结果的平均值和方差对比表明CPRNG和RC4算法产生的伪随机序列随机性能相当,相关性检测结果表明该CPRNG在不同的密钥扰动下产生的密钥各组序列几乎完全独立,设计的CPRNG能产生性能良好的伪随机数。
文摘In this paper, an approach for chaotifying a stable controllable linear system via single input state-feedback is presented. The overflow function of the system states is designed as the feedback controller, which can make the fixed point of the closed-loop system to be a snap-back repeller, thereby yields chaotic dynamics. Based on the Marotto theorem, it proves theoretically that the closed-loop system is chaotic in the sense of Li and Yorke. Finally, the simulation results are used to illustrate the effectiveness of the proposed method.
文摘In this paper, we investigate the complex dynamics of two-species Ricker-type discrete-time competitive model. We perform a local stability analysis for the fixed points and we will discuss about its persistence for boundary fixed points. This system inherits the dynamics of one-dimensional Ricker model such as cascade of period-doubling bifurcation, periodic windows and chaos. We explore the existence of chaos for the equilibrium points for a specific case of this system using Marotto theorem and proving the existence of snap-back repeller. We use several dynamical systems tools to demonstrate the qualitative behaviors of the system.
基金This work was partially supported by the National Natural Science Foundation of China(Grant No.10071043)the Hong Kong Research Grants Council under the CERG grant CityU 1115/03E+1 种基金the NSF Shandong Research Funds for Young Scientists(Grant No.03BS094)the Shandong University Scientific Research Funds for Young Staff.The authors are very happy to have this opportunity to thank the referees for helpful remarks.
文摘This paper is concerned with chaos in discrete dynamical systems governed by continuously Frechet differentiable maps in Banach spaces. A criterion of chaos induced by a regular nondegenerate homoclinic orbit is established. Chaos of discrete dynamical systems in the n-dimensional real space is also discussed, with two criteria derived for chaos induced by nondegenerate snap-back repellers, one of which is a modified version of Marotto's theorem. In particular, a necessary and sufficient condition is obtained for an expanding fixed point of a differentiable map in a general Banach space and in an n-dimensional real space, respectively. It completely solves a long-standing puzzle about the relationship between the expansion of a continuously differentiable map near a fixed point in an n-dimensional real space and the eigenvalues of the Jacobi matrix of the map at the fixed point.
