School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, China.
Institute of Decision and Game Theory, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, China.
Chaos. 2022 Oct;32(10):103106. doi: 10.1063/5.0096959.
Nonsmooth systems are widely encountered in engineering fields. They have abundant dynamical phenomena, including some results on the complex dynamics in such systems under quasiperiodically forced excitations. In this work, we consider a quasiperiodically forced piecewise linear oscillator and show that strange nonchaotic attractors (SNAs) do exist in such nonsmooth systems. The generation and evolution mechanisms of SNAs are discussed. The torus-doubling, fractal, bubbling, and intermittency routes to SNAs are identified. The strange properties of SNAs are characterized with the aid of the phase sensitivity function, singular continuous spectrum, rational frequency approximation, and the path of the partial Fourier sum of state variables in a complex plane. The nonchaotic properties of SNAs are verified by the methods of maximum Lyapunov exponent and power spectrum.
非光滑系统在工程领域中广泛存在。它们具有丰富的动力学现象，包括在准周期激励下此类系统中复杂动力学的一些结果。在这项工作中，我们考虑了一个准周期激励的分段线性振荡器，并证明了在这种非光滑系统中确实存在奇异非混沌吸引子（SNAs）。讨论了 SNAs 的产生和演化机制。确定了通向 SNAs 的环加倍、分形、冒泡和间歇路由。奇异非混沌吸引子的奇异特性通过相位灵敏度函数、奇异连续谱、有理频率逼近以及状态变量在复平面上的部分傅里叶和的路径来表征。通过最大李雅普诺夫指数和功率谱的方法验证了 SNAs 的非混沌特性。
