分数阶异结构超混沌系统完全同步与反相同步控制

摘要

以分数阶Lü混沌系统和分数阶Chen超混沌系统为例，研究了维数不同、分数阶次不相等的异结构的混沌系统和超混沌系统的完全同步和反相同步。首先，基于分数阶系统稳定性理论和非线性动力学理论，构造出相应的非线性控制器，实现了两个维数不同，分数阶次不相等异结构混沌系统与超混沌系统的完全同步和反相同步；其次，基于分数阶稳定性理论，对上述两类同步给出了严格的数学证明；最后，借助于预估-校正算法，利用数值模拟验证了所提方法的有效性。%In this paper,the complete synchronization and anti-phase synchronization between the 3-dimensional chaotic system and 4-dimensional hyper-chaotic system with different dimension and fractional order are re-searched in which the fractional-order Lü chaotic system and the fractional-order Chen hyper-chaotic system are as an example.First,Based on the fractional theory of stability and nonlinear dynamic theory.the nonlinear control-ler is designed,and by the nonlinear controller the complete synchronization and anti-phase synchronization be-tween different the 3D fractional-order chaotic system and 4D fractional-order hyper-chaotic system with different dimension and fractional order are realized.Second,based on the fractional-order theory of stability the two kind of synchronization are respectively proved strictly in mathematics.Finally,by the Predictor-Corrector scheme nu-merical simulation,the validity of the method presented in this paper is verified.