一类电路系统的分岔分析及超混沌控制研究

Study on hyperchaos control and bifurucation for a kind of circuit system

为了揭示电路系统丰富的非线性动力学行为,提高电路系统的稳定性,避免混沌或超混沌电路对元器件的危害,针对一类电路系统模型,应用现代数学中的微分方程理论和非线性动力学的方法,分析了系统发生分岔的条件,并通过数值分析验证了该理论结果。研究发现系统在一定参数条件下存在内衣马克-沙克分岔和倍周期分岔,随着参数的变化系统演化为混沌和超混沌。针对目前超混沌控制方法的研究较少,而且控制的周期轨道多是低周期轨道,提出一种节约能量并能将系统控制到高倍周期和概周期的方法,为研究许多现实离散系统模型提供了一种新的方法,对于研究电路系统提供了一条新的思路,因而具有一定的理论意义和实用价值。

In order to discover abundant nonlinear dynamics behaviors, improve the stability in circuit systems and avoid damage of the electric elements or parts by chaos and hyperchaos circuits, the model of a kind of circuit system is given and the condition of bifurcation is analyzed by ordinary equation theory and nonlinear dynamics methods. It is discovered that Y. Neimark-R. J. Sacker bifurcation and period-doubling bifurcation existed under certain parameters, which will evolve to chaos and hyperchaos with the variation of the parameters. Since less study have been carried out on hyperchaos control methods and most of the controlled periodic orbits are low periodic orbits, we propose a new method that can keep high periodic and quasiperiodic motions to hyperchaos of this system with saved energy. It is also a new method for studying the models of many practical discrete systems, which supplies a new idea for circuit system research.