Josephson结电路系统的混沌控制

Controlling the chaos of Josephson junction system

本文在考虑隧道效应的前提下,分析了含Josephson结电路系统的复杂非线性动力学,建立了系统的非线性动力学方程。根据系统的相图、分叉图及Lyapunov指数图分析了系统由周期运动进入混沌运动的过程。利用外加耦合控制器和利用非线性状态反馈反馈法两种方法实现了系统混沌运动的周期控制,得到了受控系统的周期运动相图及混沌控制控制参数变化时的分叉图。并讨论了这两种控制方法的特点。

The complex dynamics characters of the Josephson junction circuit system are studied and the tunnel effect is considered. The dynamical equation of the system is established. By the phase portraits, the motions of the system are studied under the definite parameters. And by bifurcation diagram, the route from periodic motion to chaos is studied under the presented system parameters. An adscititious coupling controller is constructed to control the chaos of the Josephson junction circuit system. The chaos of the system is controlled via adding nonlinear state feedback variables, too. The phase plane portraits and bifurcation diagram of the controlled system are obtained. The advantages of the two controlled methods are that the collect of the control signals are simple and can put on any time and the chaotic system can be asymptotically stabilized to equilibriums with small control. The orbits of the system can be controlled by these three methods according to our target.