偏移控制下Hyperjerk系统复杂振荡行为的动态分析

Dynamic Analysis of Complex Oscillation Behavior in Hyperjerk System under Offset Control

摘要: 运用非线性动力学理论和方法分析一种具有指数非线性的hyperjerk电路系统的复杂动力学行为，发现周期振荡与混沌现象共存的现象。首先，通过分析电路系统中物理参数的取值对系统复杂行为的影响，得出物理参数值对系统会产生不同的分岔现象。随着物理参数的逐渐增加，对系统周期性的影响呈现稳步递减的现象；其次，研究发现系统的复杂动力学行为对初始条件的取值也具有敏感性，但是不同初始值和物理参数动态调控下系统会产生周期与混沌现象共存的非对称混合模式簇振荡现象；同时发现一种非常罕见的气泡分岔现象。最后，对系统增加一个偏移位置常数进行控制。数值计算结果表明，偏移控制常数值对系统全局的动力学行为没有改变，只影响相应位置信号的整体相位值。

Abstract: In order to study complex dynamical behaviours behavior exhibited by the hyperjerk circuit system with nonlinear components, the complex oscillation behavior of the system is analyzed using nonlinear dynamics theory and methods. Firstly, the influence of the value of the physical parameters on the complex behavior of the system in the circuit system is analyzed, and there are different bifurcation phenomena for the system produced by the physical parameter values. The change of system periodicity is steadily decreasing as the physical parameters increase gradually. Secondly, the complex dynamical behaviours of the system are also sensitive to the values of the initial conditions. However, the system produces an asymmetric mixed mode bursting oscillation phenomenon which is the coexistence of periodic and chaotic phenomena under the dynamic regulation of different initial values and physical parameters. Meanwhile, a very rare phenomenon named bubbles of bifurcation is also found. Finally, an offset position constant is added to control the signal of the system. The numerical results indicate that the offsetting control constant value does not change the global dynamics behavior of the system, and the overall phase value of the corresponding position signal is only affected.