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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.

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)
Full Text: DOI
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