Equations for Biological Evolution

Angel Calsina, Carles Perellã

Research output: Contribution to journalArticleResearchpeer-review

26 Citations (Scopus)

Abstract

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. © 1995, Royal Society of Edinburgh. All rights reserved.
Original languageEnglish
Pages (from-to)939-958
JournalProceedings of the Royal Society of Edinburgh: Section A Mathematics
Volume125
Issue number5
DOIs
Publication statusPublished - 1 Jan 1995

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