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郭上江

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期刊论文

Hopf bifurcating periodic orbits in a ring of neurons with delays

郭上江Shangjiang Guo* Lihong Huang

Physica D 183(2003)19-44,-0001,():

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摘要/描述

In this paper, we consider a ring of neurons with self-feedback and delays. The linear stability of the model is investigated by analyzing the associated characteristic transcendental equation. Based on the normal form approach and the center manifold theory, we derive the formula for determining the properties of Hopf bifurcating slowly oscillating periodic orbits for a ring of neurons with delays, including the direction of Hopf bifurcation, stability of the Hopf bifurcating slowly oscillating periodic orbits, and so on. Moreover, by means of the symmetric bifurcation theory of delay differential equations coupled with representation theory of standard dihedral groups, we not only investigate the effect of synaptic delay of signal transmission on the pattern formation, but also obtain some important results about the spontaneous bifurcation of multiple branches of periodic solutions and their spatio-temporal patterns.

版权说明:以下全部内容由郭上江上传于   2010年01月07日 11时18分42秒,版权归本人所有。

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