Global attraction and repulsion of a heteroclinic limit cycle in three dimensional Kolmogorov maps
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 esta...
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| Format: | Conference or Workshop Item |
| Language: | English |
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Springer
2023
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| Online Access: | https://repository.londonmet.ac.uk/7928/1/heteroclinic-limit-cycles.pdf |
| Summary: | 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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