论文标题
耦合振荡器理论的最新进展
Recent Advances in Coupled Oscillator Theory
论文作者
论文摘要
我们回顾了平滑系统弱耦合振荡器的理论。然后，我们研究标准理论的应用不足并说明如何扩展的情况。为非平滑系统提供了特定的示例，该系统具有应用于Izhikevich神经元的应用。然后，我们介绍了同等减少的想法，以探索弱耦合范式无法解释的行为。在另一个示例中，我们说明如何使用同样降低的概念来理解一对相同的耦合神经元中相位锁定溶液稳定性的分叉。
We review the theory of weakly coupled oscillators for smooth systems. We then examine situations where application of the standard theory falls short and illustrate how it can be extended. Specific examples are given to non-smooth systems with applications to the Izhikevich neuron. We then introduce the idea of isostable reduction to explore behaviors that the weak coupling paradigm cannot explain. In an additional example, we show how bifurcations that change the stability of phase locked solutions in a pair of identical coupled neurons can be understood using the notion of isostable reduction.
