不变时滞线性系统的混沌反控制

针对一类具有不变时滞的线性系统,运用泰勒公式,得到系统最大李雅普诺夫(Lyapunov)指数的表达式,获得系统对初始条件敏感的判断依据.此外,构造合适的李雅普诺夫函数,基于泛函微分方程的有界性引理,得到关于系统的解有界的判断准则.结合系统敏感性和有界性的理论结果,获得不变时滞线性系统混沌化的充分条件.最后,数值仿真出最大Lyapunov指数随时滞参数变化的图形,并做出在相应时滞参数下的相图.仿真结果验证了理论结果的有效性.

Anti-control of Chaos for a Class of Linear Systems with Invariable Time-delay

A class of linear systems with invariable time-delay is studied.By the use of Taylor's formula,an expression of the maximum Lyapunov exponent for the systems is obtained,and a judgement about the sensitivity to the initial conditions is derived.Additionally,based on the boundedness lemma for general functional differential equations,a suitable Lyapunov functional is constructed and then a criteria about the boundness of the systems is obtained.Combining the theoretical results above,a theorem about the chaotification for the time-delayed systems is derived.Finally,we cifed some examples to demonstrate the effectiveness of the theoretical results by simulating the the maximum Lyapunov exponent which changes with timedelay parameters and corresponding phase diagrams.