PRT系统极限界的估计及其在混沌同步中的应用

Weiwei Wang, Jigui Jian, Zhihua Zhao
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引用次数: 1

摘要

本文讨论了Pikovski, Rabinovich和Trakhtengerts提出的描述等离子体不稳定性振幅的系统的极限界和正不变集。基于关于系统参数的广义正定和径向无界Lyapunov函数,利用广义Lyapunov函数理论,导出了PRT系统全局指数吸引集和正不变集的一个新的椭球估计和柱面域。此外,提出了双状态双输入的线性反馈控制方法,利用不等式技术实现了两个PRT系统的全局指数同步。给出了两个PRT混沌系统全局指数同步的充分代数判据。通过数值仿真验证了该方法的有效性。
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Estimations of Ultimate Bounds for the PRT System and Its Application in Chaos Synchronization
This paper is concerned with the ultimate bounds and positively invariant sets for a system describing the amplitude of a plasma instability proposed by Pikovski, Rabinovich and Trakhtengerts. Based on generalized positive definite and radially unbound Lyapunov functions with respect to the parameters of the system, we derive a new ellipsoidal estimate and a cylindrical domain of the globally exponentially attractive set and positively invariant set for the PRT system via the generalized Lyapunov function theory. In addition, linear feedback control with both two states and two inputs is proposed to realize the globally exponential synchronization of two PRT systems via inequality techniques. Some sufficient algebraic criteria for the globally exponential synchronization of two PRT chaotic systems are obtained analytically. Numerical simulations are presented to show the effectiveness of the method.
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