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Zbl 1041.68079
Guo, Shangjiang; Huang, Lihong
Hopf bifurcating periodic orbits in a ring of neurons with delays. (English)
[J] Physica D 183, No. 1-2, 19-44 (2003). ISSN 0167-2789

Summary: 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.

MSC 2000:: *68T05 Learning and adaptive systems
92B20 General theory of neural networks

Keywords: self-feedback; linear stability; characteristic transcendental equation

Cited in: Zbl 1263.34100

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