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

Anatoli F. Ivanov; Bernhard Lani-Wayda

doi:10.3934/dcds.2004.11.667

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

Anatoli F. Ivanov, Bernhard Lani-Wayda

Penn State Wilkes-Barre

Research output: Contribution to journal › Article › peer-review

9 Citations (SciVal)

Abstract

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.

Original language	English (US)
Pages (from-to)	667-692
Number of pages	26
Journal	Discrete and Continuous Dynamical Systems
Volume	11
Issue number	2-3
DOIs	https://doi.org/10.3934/dcds.2004.11.667
State	Published - 2004

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcds.2004.11.667

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title = "Periodic solutions for three-dimensional non-monotone cyclic systems with time delays",

abstract = "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.",

author = "Ivanov, {Anatoli F.} and Bernhard Lani-Wayda",

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AU - Ivanov, Anatoli F.

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AB - 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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JF - Discrete and Continuous Dynamical Systems

IS - 2-3

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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