Periodic solutions for three-dimensional non-monotone cyclic systems with time delays | Zendy

Anatoli F. Ivanov | Zendy; Bernhard LaniWayda | Zendy

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Periodic solutions for three-dimensional non-monotone cyclic systems with time delays

Author(s) -

Anatoli F. Ivanov,

Bernhard LaniWayda

Publication year - 2004

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2004.11.667

Subject(s) - monotone polygon , mathematics , fixed point theorem , instability , monotonic function , symmetry (geometry) , fixed point , mathematical analysis , pure mathematics , physics , geometry , mechanics

We study a model for three cyclically coupled neurons with eventually negative delayed feedback, and without symmetry or monotonicity properties. Periodic solutions are obtained from the Schauder fixed point theorem. It turns out that, contrary to lower dimensional cases, instability at zero does not exclude monotonously decaying solutions.

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