Zhou Douglas, Rangan Aaditya V, Sun Yi, Cai David
Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 1):031918. doi: 10.1103/PhysRevE.80.031918. Epub 2009 Sep 28.
It has been shown that a single standard linear integrate-and-fire (IF) neuron under a general time-dependent stimulus cannot possess chaotic dynamics despite the firing-reset discontinuity. Here we address the issue of whether conductance-based, pulsed-coupled network interactions can induce chaos in an IF neuronal ensemble. Using numerical methods, we demonstrate that all-to-all, homogeneously pulse-coupled IF neuronal networks can indeed give rise to chaotic dynamics under an external periodic current drive. We also provide a precise characterization of the largest Lyapunov exponent for these high dimensional nonsmooth dynamical systems. In addition, we present a stable and accurate numerical algorithm for evaluating the largest Lyapunov exponent, which can overcome difficulties encountered by traditional methods for these nonsmooth dynamical systems with degeneracy induced by, e.g., refractoriness of neurons.
研究表明，单个标准线性积分发放（IF）神经元在一般的时间依赖刺激下，尽管存在发放重置不连续性，但仍无法呈现混沌动力学。在此，我们探讨基于电导的脉冲耦合网络相互作用是否能在IF神经元群体中诱导混沌。通过数值方法，我们证明全对全、均匀脉冲耦合的IF神经元网络在外部周期性电流驱动下确实能够产生混沌动力学。我们还对这些高维非光滑动力系统的最大Lyapunov指数进行了精确表征。此外，我们提出了一种稳定且准确的数值算法来评估最大Lyapunov指数，该算法能够克服传统方法在处理这些由神经元不应期等因素导致简并的非光滑动力系统时所遇到的困难。
