【作者】 胥红星；

【导师】 舒永录；

【作者基本信息】 重庆大学 ， 基础数学， 2009， 硕士

【摘要】 混沌系统的最终界在混沌系统的定性行为的研究中有着重要的作用,若我们可以找到一个混沌系统的全局吸引集,则可以断定在这个全局吸引集之外不会存在该系统其它的平衡位置、周期解、概周期解、游荡回复解和其它任何吸引子,这可以简化对一个系统基本的动力学性质的分析和研究,同样在混沌系统的控制和同步中有着广泛的用途。利用广义Lyapunov函数理论和优化理论研究了三个混沌系统的全局吸引集和正向不变集。对于一个新混沌系统,分析了该系统的基本的混沌动力学行为,得到了一个三维椭球形式的全局吸引集和正向不变集,从数学理论上给予了严格的证明,且估计了该系统关于x ? z和y ? z在二维中的有界性。对于Qi混沌系统和Lorenz-Stenflo混沌系统,我们采用了同样的方法得到了不同形式的一系列的椭球型估计式,然后在将得到的结果应用到同步上,实现了系统的全局同步,最后利用Matlab进行仿真,验证了理论的有效性。更多还原

【Abstract】 The ultimate bound of a chaotic system is important for the study of the qualitative behavior of a chaotic system. If we can show that a system under consideration has a globally attractive set, then we know that the system cannot have equilibrium points, periodic solutions, quasi-periodic solutions, or other chaotic attractors outside the globally attractive set. This greatly simplifies the analysis of the dynamical properties of the system. The ultimate bound also plays an important role in designing scheme for chaos control and chaos synchronization.This paper investigates the ultimate bound and positively invariant set for three chaotic systems via the generalized Lyapunov function and optimization.Some basic dynamical properties are investigated for a new chaotic system, we derive a three-dimensional ellipsoidal ultimate bound and positively invariant set and prove the existence in mathematical theory. And the two-dimensional bound with respect to x ? z and y ? zare established.With the help of the same method, we get the many different ellipsoidal-like formulas for the Qi chaotic system and the Lorenz-Stenflo chaotic system. Then the result is applied to the study of chaos synchronization and the globally synchronization of the two systems is achieved. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme更多还原