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Equations for biological evolution*

Published online by Cambridge University Press:  14 November 2011

Angel Calsina  and
Carles Perelló
Angel Calsina
Affiliation:
Departament de Matematiques, Universitat Autonoma de Barcelona, Edifici C, 08193 Bellaterra (Barcelona), Spain
Carles Perelló
Affiliation:
Departament de Matematiques, Universitat Autonoma de Barcelona, Edifici C, 08193 Bellaterra (Barcelona), Spain
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Extract

In this paper we consider mathematical models inspired by the mechanisms of biological evolution. We take populations which are subject to interaction and mutation. In the cases we consider, the interaction is through competition or through a prey-predator relationship. The models consider the specific characteristics as taking values in real intervals and the equations are of the integro—differential type. In the case of competition, thanks to the fact that some of the equations have solutions which are quite explicit, we succeed in proving the existence of attracting stationary solutions. In the case of prey and predator, using techniques of dynamical systems in infinite-dimensional spaces, we succeed in showing the existence of a global attractor, which in some instances reduces to a point. Our analysis takes into account having δ distributions, corresponding to all individuals having the same characteristics, as possible populations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 5 , 1995 , pp. 939 - 958
Copyright
Copyright © Royal Society of Edinburgh 1995

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