Fudan University, Shanghai Key Laboratory for Contemporary Applied Mathematics, Shanghai, 200433, PR China.
Int J Neural Syst. 2009 Dec;19(6):425-35. doi: 10.1142/S0129065709002129.
Fireflies, as one of the most spectacular examples of synchronization in nature, have been investigated widely. In 1990, Mirollo and Strogatz proposed a pulse-coupled oscillator model to explain the synchronization of South East Asian fireflies (Pteroptyx malaccae). However, transmission delays were not considered in their model. In fact, when transmission delays are introduced, the dynamic behaviors of pulse-coupled networks change a lot. In this paper, pulse-coupled oscillator networks with delayed excitatory coupling are studied. A concept of synchronization, named weak asymptotic synchronization, which is weaker than asymptotic synchronization, is proposed. We prove that for pulse-coupled oscillator networks with delayed excitatory coupling, weak asymptotic synchronization cannot occur.
萤火虫作为自然界中最壮观的同步现象之一，已经被广泛研究。1990 年，Mirollo 和 Strogatz 提出了一个脉冲耦合振荡器模型来解释东南亚萤火虫（Pteroptyx malaccae）的同步现象。然而，他们的模型中没有考虑传输延迟。事实上，当引入传输延迟时，脉冲耦合网络的动态行为会发生很大变化。在本文中，研究了具有延迟兴奋耦合的脉冲耦合振荡器网络。提出了一个名为弱渐近同步的同步概念，它比渐近同步弱。我们证明了对于具有延迟兴奋耦合的脉冲耦合振荡器网络，弱渐近同步不可能发生。
