中文摘要：

非线性动力学系统的混沌同步,一般采用单向线性耦合的控制方式,对于函数耦合方式研究的比较少.这就存在一个问题,对于非线性动力学系统,在线性耦合实现混沌同步后,是否其他函数的耦合方式都可以实现混沌同步？本文对于一类非线性动力学系统,研究了其线性耦合同步与函数耦合同步的关系,证明当线性耦合实现同步后,函数在满足一定的条件下,可以通过函数耦合实现系统的混沌同步.最后对于Duffing系统采用两种函数耦合进行了仿真计算,证明了结论的正确性.

英文摘要：

To realize the synchronization of nonlinear dynamical system,the general control method is unidirectional linear coupling.Research on function coupling of chaos synchronization is not enough,so there arises a question：for nonlinear dynamical system,if chaos synchronization is realized by linear coupling,whether can any type of function coupling always make the system go to chaos synchronization？ In this paper,a class of nonlinear dynamical system is considered and the relation between linear coupling and function coupling is investigated.It is proved that if linear coupling can make chaos synchronization,then any function satisfying some conditions can do so too.The condition is given and proved.Finally for Duffing system,three coupling functions are used to prove the analytical result.The simulation results show that the conclusion is correct.