一个混沌系统的单输入指数自适应同步分析

The Analysis of a Single Exponential Input Adaptive Synchronization of a Chaotic System

首先引入一个含有乘积项系统参数的混沌系统.对新的吸引子的基本性质用相图、平衡点及稳定性、李亚谱诺夫指数谱、分岔图、Poincaré截面进行了详细分析.然后对系统参数都为正时的系统的界进行了估计,并给出系统界的表达式.由于系统中含有乘积项参数,当参数未知时,同步新系统会比较困难.文中用一个带有自适应参数更新的单输入控制器取得了系统的同步.最后,用数值仿真验证提出方法有效性.

This paper firstly presents a chaotic system including a product term of system parameters. Basic dynamical properties ofthe attractor are demonstrated in terms of phase portrait, equilibria and stability, Lyapunov exponent spectrum, bifurcation diagram andpoincaré mapping. Then, the bound of this system is estimated for all the positive values of its parameters and the expression of the boundis illustrated. Owing to a product term of system parameters, it can be predicted that synchronization of the new system becomes more diffi-culty by taking account of uncertain system parameters. In this paper, the exponential synchronization between two identical chaotic sys-tems by applying single input controller associated with system parameter update laws is proposed. At last, numerical studies are providedto illustrate the effectiveness of the presented scheme.