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

Attractors in continuous –time switching networks

Tomáš Gedeon 1,

1. 

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

Received  February 2002 Revised  January 2003 Published  March 2003

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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