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

Article Contents

2004, Volume 11, Issue 2&3: 667-692. Doi: 10.3934/dcds.2004.11.667

This issue Previous Article On the profile of solutions for an elliptic problem arising in nonlinear optics Next Article Non-collision periodic solutions of forced dynamical systems with weak singularities

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

Anatoli F. Ivanov^1, and
Bernhard Lani-Wayda^2,

1.
Department of Mathematics, Pennsylvania State University, P.O. Box PSU, Lehman, PA 18627
2.
Mathematisches Institut der Universität Giessen, Arndtstr. 2, 35392 Giessen

Received: December 31, 2002

Revised: February 29, 2004

Published: August 2004

Abstract Related Papers Cited by

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.

Keywords:

Mathematics Subject Classification: Primary: 34K13; Secondary: 92B20.

Citation:

Article Metrics

HTML views() PDF downloads(42) Cited by(0)

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

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

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

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content