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Global attraction and repulsion of a heteroclinic limit cycle in three dimensional Kolmogorov maps

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Hou, Zhanyuan (2023) Global attraction and repulsion of a heteroclinic limit cycle in three dimensional Kolmogorov maps. In: 26th ICDEA: Advances in Discrete Dynamical Systems, Difference Equations and Applications, 26-30 July 2021, Sarajevo, Bosnia and Herzegovina.

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Abstract

There is a recent development in the carrying simplex theory for competitive maps: under some weaker conditions a map has a modified carrying simplex (one of the author's latest publications). In this paper, as one of the applications of the modified carrying simplex theory, a criterion is established for a three dimensional Kolmogorov map to have a globally repelling (attracting) heteroclinic limit cycle. As a concrete example, a discrete competitive model is investigated to illustrate the above criteria for global repulsion (attraction) of a hetericlinic limit cycle.

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