不同维不同阶的分数阶混沌系统同步及仿真

摘要

分数阶混沌系统同步在安全保密通信等领域有着重要的应用价值和研究意义.对不同维不同阶的分数阶混沌系统之间的广义同步,根据主动控制和分数阶系统稳定性理论设计控制器实现同步.先将两个分数阶混沌系统分解为线性和非线性部分之和,用主动控制构造同步误差方程,然后利用分数阶线性时不变系统稳定性理论设计控制器,实现不同维不同阶分数阶混沌系统之间的广义同步,再用分数阶微分的Caputo定义和分数阶微分方程的预测校正数值解法进行数值仿真,实现三维Chen系统和四维超Lorenz系统间的广义同步.仿真结果表明了提出方法的有效性.%Synchronization of fractional-order chaotic system has great merit of application and research in security communications and other fields. This paper mainly investigates synchronization and simulation of fractional-order chaotic system with different dimension and different order, and designs a synchronization controller based on active control and stability theory of fractional-order system. Firstly, the chaotic system was separated into two parts, the linear part and the nonlinear part, and the synchronization err equation was built up based on active control theory. Then the controller was obtained based on stability theory of the linear time invariant fractional - order systems, a method for generalizing synchronization of fractional-order chaotic system with different dimension and different orders is proposed. Synchronization 3-dimensions fractional-order chaotic Chen system and 4-dimensions fractional-order hyperchaotic Lorenz system is realized based on the Caputo definition of fractional derivatives and the numerical method of predictor-corrector scheme for fractional differential equations. Numerical simulations show the effectiveness of the developed approach.