Mircheski Petar, Zhu Jinjie, Nakao Hiroya
Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan.
State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China.
Chaos. 2023 Oct 1;33(10). doi: 10.1063/5.0161119.
We present a phase-amplitude reduction framework for analyzing collective oscillations in networked dynamical systems. The framework, which builds on the phase reduction method, takes into account not only the collective dynamics on the limit cycle but also deviations from it by introducing amplitude variables and using them with the phase variable. The framework allows us to study how networks react to applied inputs or coupling, including their synchronization and phase locking, while capturing the deviations of the network states from the unperturbed dynamics. Numerical simulations are used to demonstrate the effectiveness of the framework for networks composed of FitzHugh-Nagumo elements. The resulting phase-amplitude equations can be used in deriving optimal periodic waveforms or introducing feedback control for achieving fast phase locking while stabilizing the collective oscillations.
我们提出了一个用于分析网络动力系统中集体振荡的相位-振幅约简框架。该框架基于相位约简方法构建，不仅考虑了极限环上的集体动力学，还通过引入振幅变量并将其与相位变量一起使用，考虑了与极限环的偏差。该框架使我们能够研究网络如何响应施加的输入或耦合，包括它们的同步和锁相，同时捕捉网络状态与未受扰动动力学的偏差。数值模拟用于证明该框架对由FitzHugh-Nagumo元件组成的网络的有效性。所得的相位-振幅方程可用于推导最优周期波形或引入反馈控制，以在稳定集体振荡的同时实现快速锁相。
