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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:

34K13 Periodic solutions to functional-differential equations
34K20 Stability theory of functional-differential equations
34K17 Transformation and reduction of functional-differential equations and systems, normal forms
92B20 Neural networks for/in biological studies, artificial life and related topics
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