# American Institute of Mathematical Sciences

March  2004, 11(2&3): 667-692. doi: 10.3934/dcds.2004.11.667

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

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

Received  January 2003 Revised  March 2004 Published  June 2004

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.
Citation: Anatoli F. Ivanov, Bernhard Lani-Wayda. Periodic solutions for three-dimensional non-monotone cyclic systems with time delays. Discrete and Continuous Dynamical Systems, 2004, 11 (2&3) : 667-692. doi: 10.3934/dcds.2004.11.667
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