Chaotic dynamics of an integrate-and-fire circuit with periodic pulse-train input
Chaotic dynamics of an integrate-and-fire circuit with periodic pulse-train input
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DOI：
10.1109/tcsi.2003.811015
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发表时间：
2003-06
影响因子：
5.1
通讯作者：
Wei Lin;J. Ruan
中科院分区：
文献类型：
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作者：
Wei Lin;J. Ruan
本文介绍了中野等人（1999）首次提出的具有两个状态的起搏神经元型积分激发电路的工作原理。该电路的动力学可以用一个标准的脉冲微分方程来描述，并用于模拟脉冲耦合神经网络的演化。应用Marotto定理（1978），我们从理论上证明了当参数进入某些区域时，电路会变得混沌。我们发现，电路不表现出混沌动力学与小周期的脉冲串输入，但混沌现象出现与周期的增加。进一步研究了该回路与符号动力学回路之间的关系。数值模拟和相应的计算，作为说明性的例子，加强我们的理论证明和理论。
In this brief, we introduce the working principle of a pacemaker neuron type integrate-and-fire circuit having two states with a periodic pulse-train input, first proposed by Nakano et al. (1999). The dynamics of this circuit can be described by a standard impulsive differential equation and applied to simulate the evolution of the pulse-coupled neural networks. By applying the Marotto theorem (1978), we theoretically prove that the circuit becomes chaotic as the parameters enter some regions. We find that the circuit does not exhibit chaotic dynamics with a small period of the pulse-train input but that a chaotic phenomenon appears with increase of the period. The relations between this circuit and that of symbolic dynamics are further investigated. Numerical simulations and corresponding calculation, as illustrative examples, reinforce our theoretical proof and theory.