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Stability of nonlinear waves in a ring of neurons with delays. (English) Zbl 1132.34048
In this article a ring of identical neurons with self-feedback and delays is considered. Based on a former existence result of a bifurcation branch of periodic solutions, the authors obtain formulas about the bifurcation direction and stability of the periodic solutions. In particular, properties of phase-locked oscillatory waves, mirror-reflected and standing waves are discussed. The main tools used in the article are normal form theory and center manifold theory.

MSC:
34K13Periodic solutions of functional differential equations
34K20Stability theory of functional-differential equations
34K17Transformation and reduction of functional-differential equations and systems; normal forms
92B20General theory of neural networks (mathematical biology)
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References:
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