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Homotopy Techniques in Stability Problems of Delay-Diffusion Volterra Models

In: Biomathematics and Related Computational Problems

Author

Listed:
  • Edoardo Beretta

    (University of Urbino, Institute of Biomathematics)

  • Yasuhiro Takeuchi

    (Shizuoka University, Department of Applied Mathematics, Faculty of Engineering)

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.

Suggested Citation

  • Edoardo Beretta & Yasuhiro Takeuchi, 1988. "Homotopy Techniques in Stability Problems of Delay-Diffusion Volterra Models," Springer Books, in: Luigi M. Ricciardi (ed.), Biomathematics and Related Computational Problems, pages 245-254, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-2975-3_22
    DOI: 10.1007/978-94-009-2975-3_22
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