标题： 弱耦合极限环振荡器的快速全局同步最优耦合函数 显示英文标题

标题： Optimal coupling functions for fast and global synchronization of weakly coupled limit-cycle oscillators

摘要： 我们提出了一种优化耦合函数的方法，以实现一对弱耦合极限环振荡器之间的快速且全局的同步。 我们的方法基于相位约化，它为相互耦合振荡器的同步动力学提供了简洁的低维表示，包括耦合依赖于振荡器过去时间序列的情况。 我们首先描述了一对相同振荡器的方法，然后将其推广到略微不同的振荡器情况。 耦合函数通过两个优化步骤来设计其形式和幅度，其中幅度被数值优化以在总功率约束下最小化平均收敛时间。 我们使用FitzHugh-Nagumo和Rössler振荡器作为例子，对使用优化后的耦合函数的同步动力学进行了数值模拟。 我们证明了由所提出方法优化的耦合函数比以前的方法能更有效地实现全局同步。 显示英文摘要

摘要： We propose a method for optimizing mutual coupling functions to achieve fast and global synchronization between a pair of weakly coupled limit-cycle oscillators. Our method is based on phase reduction that provides a concise low-dimensional representation of the synchronization dynamics of mutually coupled oscillators, including the case where the coupling depends on past time series of the oscillators. We first describe a method for a pair of identical oscillators and then generalize it to the case of slightly nonidentical oscillators. The coupling function is designed in two optimization steps for the functional form and amplitude, where the amplitude is numerically optimized to minimize the average convergence time under a constraint on the total power. We perform numerical simulations of the synchronization dynamics with the optimized coupling functions using the FitzHugh-Nagumo and R\"{o}ssler oscillators as examples. We show that the coupling function optimized by the proposed method can achieve global synchronization more efficiently than the previous methods.