噪音诱导的混沌震荡  

Noise Induced Chaotic Bursting

作　　者：李骥 李萍[1] Li Ji;Li Ping(School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China)

机构地区：[1]华中科技大学数学与统计学院,武汉430074

出　　处：《数学理论与应用》2023年第1期44-63,共20页Mathematical Theory and Applications

基　　金：National Natural Science Foundation of China(No.12171174)。

摘　　要：周期与混沌震荡行为常见于神经元或者激素细胞.该行为的组成成分为抑止态和反复放电态,并且在这两种状态之间反复切换.对于此类行为的兴趣由来已久.随机外力对于在很多情况下都会产生不可忽略的影响.本文研究一类一致有界随机外力对于放电和震荡行为的影响,解释一种由一致有界随机外力产生混沌震荡的机制,并给出数值模拟用于佐证.Periodic or chaotic bursting behavior is commonly observed in neurons and endocrine cells,consisting of recurrent transitions between quiescent states and repetitive spikings,and has been of interest for a long time.Stochastic forcing is known to have nonnegligible influence in many cases.In this paper we study the effect of uniformly bounded noise on the spike and burst behavior and explain the mechanism how uniformly bounded noise generates chaotic bursting.Numerical simulation is provided to support the underlying mechanism.

关 键 词：随机动力系统 震荡 不变流形 奇异摄动 混沌 

分 类 号：Q424[生物学—神经生物学]