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arXiv · 2209.11132

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

Zhanyuan Hou
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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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Zhanyuan Hou. 2022-09-22. Global attraction and repulsion of a heteroclinic limit cycle in three dimensional Kolmogorov maps. https://arxiv.org/abs/2209.11132

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