Talathi Sachin S, Hwang Dong-Uk, Miliotis Abraham, Carney Paul R, Ditto William L
J. Crayton Pruitt Department of Biomedical Engineering, University of Florida, Gainesville, Florida 32611, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Aug;80(2 Pt 1):021908. doi: 10.1103/PhysRevE.80.021908. Epub 2009 Aug 11.
Pulse coupled oscillators (PCOs) represent an ubiquitous model for a number of physical and biological systems. Phase response curves (PRCs) provide a general mathematical framework to analyze patterns of synchrony generated within these models. A general theoretical approach to account for the nonlinear contributions from higher-order PRCs in the generation of synchronous patterns by the PCOs is still lacking. Here, by considering a prototypical example of a PCO network, i.e., two synaptically coupled neurons, we present a general theory that extends beyond the weak-coupling approximation, to account for higher-order PRC corrections in the derivation of an approximate discrete map, the stable fixed point of which can predict the domain of 1:1 phase locked synchronous states generated by the PCO network.
脉冲耦合振荡器（PCOs）是许多物理和生物系统中普遍存在的模型。相位响应曲线（PRCs）提供了一个通用的数学框架，用于分析这些模型中产生的同步模式。目前仍缺乏一种通用的理论方法来解释高阶PRCs在PCOs产生同步模式过程中的非线性贡献。在这里，通过考虑一个PCO网络的典型例子，即两个通过突触耦合的神经元，我们提出了一种超越弱耦合近似的通用理论，以解释在推导近似离散映射时的高阶PRC修正，该映射的稳定不动点可以预测PCO网络产生的1:1锁相同步状态的域。
