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Attractors in coherent systems of differential equations |
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| Authors: | David Angeli Morris W. Hirsch Eduardo D. Sontag |
| Affiliation: | a Dept. of Electrical and Electronic Engineering, Imperial College, United Kingdom b Dip. di Sistemi e Informatica, Università di Firenze, Italy c Dept. of Mathematics, University California, Berkeley, United States d Dept. of Mathematics, University of Wisconsin, Madison, United States e Dept. of Mathematics, Rutgers University, United States |
| Abstract: | Attractors of cooperative dynamical systems are particularly simple; for example, a nontrivial periodic orbit cannot be an attractor, and orbits are nowhere dense. This paper provides characterizations of attractors for the wider class of coherent systems, defined by the property that all directed feedback loops are positive. Several new results for cooperative systems are obtained in the process. Connections with biological models are discussed. |
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