期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
Chaos Controlling in a Class of Nonlinear Electrical Oscillator
摘要/Abstract
研究了一类非线性振荡电路系统的复杂动力学行为.基于基尔霍夫定律建立了一类非线性周期振荡电路的动力学方程.利用Poincaré 映射图分析了系统混沌吸引子的特性,通过分岔图和Lyapunov指数谱揭示了此类系统由倍周期分岔通向混沌的过程,并且验证了该系统的分岔图与Lyapunov指数谱是完全吻合的.最后,通过非线性反馈控制方法对非线性电路系统中的混沌状态进行了有效的控制,结果表明,通过选取适宜的控制参数可以将系统控制到不同的稳定的周期轨道.
The complex dynamics behavior of a class of nonlinear electrical oscillator described by Duffing's equation is studied.The dynamical equation of the system is established by using Kirchhoff's law.The characteristic of chaotic attractors of the system are analyzed by the Poincaré sections.Routes from doubling-periodic bifurcation to chaos are analyzed by the bifurcation diagram and Lyapunov exponents,and the Lyapunov exponents corresponded to bifurcation diagrams of the system are confirmed.A technique of non-linear feedback control approach to control chaos is to be given,which can switch the chaotic motion to the desired periodic orbits effectively.Based on the non-linear feedback control,the different stable periodic orbits are obtained by adjusting the feedback coefficients.