Abstract This paper introduces and investigates the dynamics of a thin magnetostrictive actuator with quintic nonlinearity. The energy balance method is used to carry out the motion equation of the system. The analytical solutions and amplitude responses of the system are exanimated using the multiple time scale method. The dynamical behavior of the system is explored with the help of common nonlinear tools such as bifurcation diagrams with Lyapunov exponents, time series plots, phase portraits and basin of attraction. The bifurcation diagrams reveal that the system under study exhibits complicated dynamics including crisis route to chaos, multistability and antimonotonicity. To validate the theoretical and numerical analyses, an electronic circuit capable to describe the dynamics of the system is designed and implemented in PSpice software. A very good agreement is observed between PSpice based circuit simulations and theoretical/numerical results.

中文翻译：

---

在具有五次非线性的薄磁致伸缩致动器系统中引起吸引子共存的滞后动力学

摘要 本文介绍并研究了具有五次非线性的薄磁致伸缩致动器的动力学。采用能量平衡法来进行系统的运动方程。系统的解析解和幅度响应使用多时间尺度方法进行检验。系统的动力学行为是在常用非线性工具的帮助下探索的，例如带李雅普诺夫指数的分岔图、时间序列图、相图和吸引力盆。分叉图表明，所研究的系统表现出复杂的动力学，包括通往混沌的危机路径、多重稳定性和反单调性。为了验证理论和数值分析，在 PSpice 软件中设计并实现了能够描述系统动力学的电子电路。