分数阶与整数阶混沌系统的同步与反同步

摘要

为了建立起整数阶与分数阶系统的桥梁,推进分数阶系统的应用,本文采用了滑模控制理论研究了一类整数阶与分数阶混沌系统的同步与反同步.文中,设计了一个新的滑模控制器,该控制器适用于一类系统,具有较好的鲁棒性,并且给出了严格的数学证明.本文实现了整数阶Sprott系统和分数阶Chen系统的同步和整数阶吕系统和分数阶Liu系统的反同步.这两个例子有效的证明了所提理论的可行性和正确性.同时,也将同步与反同步的概念统一在一起.%In order to build up the bridge between fractional-order and integer order chaotic system,and promote the application of fractional-order system,we brought attention to synchronization and anti-synchronization of fractional-order and integer order chaotic system by using sliding mode control theory.A novel sliding mode controller was presented,which is suitable for a class of systems,including theatrical analysis.Furthermore,we carried out two typical examples,which are synchronization of Sprott system,fractional-order Chen system,anti-synchronization of Lv system and fractional-order Liu system.All of the above analyses prove the effectiveness and feasibility.Simultaneously,we unified the concept of synchronization and anti-synchornization.