Homotopy Techniques in Stability Problems of Delay-Diffusion Volterra Models

Edoardo Beretta and Yasuhiro Takeuchi
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Edoardo Beretta: University of Urbino, Institute of Biomathematics
Yasuhiro Takeuchi: Shizuoka University, Department of Applied Mathematics, Faculty of Engineering

A chapter in Biomathematics and Related Computational Problems, 1988, pp 245-254 from Springer

Abstract: Abstract We consider two models from population dynamics consisting of delay-Volterra patches connected by discrete diffusion and we show that the homotopy techniques can be applied to derive sufficient conditions for the existence of a positive equilibrium globally asymptotically stable. In section 1 we introduce the meaning of patches connected by discrete diffusion. Particurlarly we present two models: in the first n biological species (n ≥ 2) live in two different delay-Volterra patches with possibility of discrete diffusion between the patches. In the second model we consider n different single species patches (n ≥ 2) interconnected by discrete diffusion. In section 2, by a suitable homotopy function, we derive the sufficient conditions for the existence of a positive equilibrium of the first model in the case of two symbiotic delay-Volterra patches. In section 3 we show how to apply the homotopy technique to the second model.

Keywords: Linear Complementarity Problem; Positive Equilibrium; Global Asymptotic Stability; Trivial Equilibrium; Liapunov Function (search for similar items in EconPapers)
Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-2975-3_22

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DOI: 10.1007/978-94-009-2975-3_22

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