Attractors in continuous –time switching networks

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June 2003, 2(2): 187-209. doi: 10.3934/cpaa.2003.2.187

Attractors in continuous –time switching networks

1.	Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717, United States

Received February 2002 Revised January 2003 Published March 2003

Abstract
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We consider a system of equations with discontinuous right hand side, which arise as models of gene and neural networks. We study attractors in $R^4$ which lie in a set of orthants in the form of figure eight. We find that if the attractor is symmetric with respect to these two loops, then the only possible attractor is a periodic orbit which traverses both loops once. We show that without the symmetry the set of admissible attractors include periodic orbits which follow one loop $k$ times and other loop once, for any $k$. However, we also show that no trajectory in an attractor can traverse both loops more then once in a row.

Keywords: additive neural networks., Attractors, continuous-time switching networks.

Mathematics Subject Classification: 34C25, 34D45, 92B2.

Citation: Tomáš Gedeon. Attractors in continuous –time switching networks. Communications on Pure & Applied Analysis, 2003, 2 (2) : 187-209. doi: 10.3934/cpaa.2003.2.187

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