Topological degree in the generalized Gause prey-predator model

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:410

Article

Makarenkov, Oleg

关键词: Gause prey-predator model;    Topological degree;    T-irreversibility theorem;    Periodic solution;    Nonuniqueness of solutions;    Perturbation approach;    Asymptotic stability;   

DOI  :  10.1016/j.jmaa.2013.08.052

来源: Elsevier

【 摘 要 】

We consider a generalized Gause prey-predator model with T-periodic continuous coefficients. In the case where the Poincare map 7, over time T is well defined, the result of the paper can be explained as follows: we locate a subset U of R-2 such that the topological degree d(I - P, U) equals to +1. The novelty of the paper is that the later is done under only continuity and (some) monotonicity assumptions for the coefficients of the model. A suitable integral operator is used in place of the Poincare map to cope with possible nonuniqueness of solutions. The paper, therefore, provides a new framework for studying the generalized Gause model with functional differential perturbations and multi-valued ingredients. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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