多重穩定性對生物擺動器的延遲、耦合強度和凹凸性之關係

Abstract

我們研究了對於兩個Mirollo-Strogatz-type的擺動器系統中耦合強度係數、延遲時間和其函數凹凸性之間的互相影響。對於延遲函數是凹向上的擺動器，我們將可以得到一個關於激進耦合與壓抑耦合的完整的相圖。特別地，我們證明出加了延遲時間與激進耦合在一個擺動器上，將會產生了一個多重穩定的同步化。在另外一方面，對於加了延遲時間的壓抑耦合會產生同相同步化的情形是不穩定的。

We study the interaction between coupling strengths, delay and concavity for a pair of two Mirollo-Strogatz-type oscillators. For a pair of two concave oscillators with a nonzero delay, the complete phase diagrams with respect to both inhibitory and excitatory coupling are given. In particular, we prove that the delay and excitatory coupling induce multistable synchronization for such system. On the other hand, the in-phase synchronization is shown to be unstable for inhibitory coupling if the delay is not zero.