Takata Shohei, Kato Yuzuru, Nakao Hiroya
Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan.
Chaos. 2021 Sep;31(9):093124. doi: 10.1063/5.0054603.
Optimal entrainment of limit-cycle oscillators by strong periodic inputs is studied on the basis of the phase-amplitude reduction and Floquet theory. Two methods for deriving the input waveforms that keep the system state close to the original limit cycle are proposed, which enable the use of strong inputs for entrainment. The first amplitude-feedback method uses feedback control to suppress deviations of the system state from the limit cycle, while the second amplitude-penalty method seeks an input waveform that does not excite large deviations from the limit cycle in the feedforward framework. Optimal entrainment of the van der Pol and Willamowski-Rössler oscillators with real or complex Floquet exponents is analyzed as examples. It is demonstrated that the proposed methods can achieve considerably faster entrainment and provide wider entrainment ranges than the conventional method that relies only on phase reduction.
基于相幅缩减和弗洛凯理论，研究了强周期输入对极限环振荡器的最优同步。提出了两种推导使系统状态接近原始极限环的输入波形的方法，这使得能够使用强输入来实现同步。第一种幅度反馈方法使用反馈控制来抑制系统状态与极限环的偏差，而第二种幅度惩罚方法在前馈框架中寻找不会激发与极限环有大偏差的输入波形。以具有实或复弗洛凯指数的范德波尔振荡器和威廉姆斯基 - 罗斯勒振荡器的最优同步为例进行了分析。结果表明，与仅依赖相位缩减的传统方法相比，所提出的方法能够实现显著更快的同步，并提供更宽的同步范围。
