一类位于加周期分岔中的貌似混沌的随机神经放电节律的识别  

Identification of a stochastic neural firing rhythm lying in period-adding bifurcation and resembling chaos

作　　者：古华光 惠磊[1] 贾冰[2] 

机构地区：[1]陕西师范大学物理学与信息技术学院,西安710062 [2]陕西师范大学生命科学学院,西安710062

出　　处：《物理学报》2012年第8期72-81,共10页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11072135;10772101;10432010;30300107);中央高等学校基本科研基金(批准号:GK200902025)资助的课题~~

摘　　要：识别非周期神经放电节律是混沌还是随机一直是一个重要的科学问题.在神经起步点实验中发现了一类介于周期k和周期k+1(k=1,2)节律之间非周期自发放电节律,其行为是长串的周期k簇和周期k+1簇的交替.确定性理论模型Chay模型展示出了周期k和周期k+1节律的共存行为.噪声在共存区诱发出了与实验结果类似的非周期节律,说明该类节律是噪声引起的两类簇的跃迁.非线性预报及其回归映射揭示该节律具有确定性机理;将两类簇分别转换为0和1得到一个二进制序列,对该序列进行概率分析获得了两类簇跃迁的随机机理.这不仅说明该节律是具有确定性结构的随机节律而不是混沌,还为深入识别现实神经系统的混沌和随机节律提供了典型示例和有效方法.To identify non-periodic neural rhythm to be chaos or stochasticity has been an important scientific thesis. A kind of non- periodic spontaneous firing pattern, whose behavior is transition between period-k burst in a string and period-k ＋ 1 burst in a string （k = 1, 2）, lying between period-k bursting pattern and period-k ＋ 1 bursting pattern, is found in the experimental neural pacemaker. The deterministic structures of the firing are identified by nonlinear prediction and first return map of the interspike intervals （ISis） series. The co-existence of the period-k bursting and period-k ＋ 1 bursting is manifested in the deterministic theoretical neuronal model, Chay model. Non-periodic firing patterns similar to the experimental observation are simulated in the co-existing parameter region, implying that the firing pattern is transition between two kinds of bursts induced by noise. A binary series can be acquired by transforming two kinds of bursts to symbols 0 and 1, respectively. The stochastic dynamics within the transitions between two kinds of bursts are detected by probability analysis on the binary series. It not only shows that the rhythm is stochastic firing with deterministic structures instead of chaos, but also provides the typical examples and effective methods to intensively identify the chaotic and stochastic firing patterns in a real nervous system.

关 键 词：混沌 随机节律 神经放电 加周期分岔 

分 类 号：Q42[生物学—神经生物学]