| Volume 15, Number 2, 2025, Pages - DOI：10.11948/JAAC-2024-0107 |
| Bifurcations of codimension three in a Leslie-Gower type predator-prey system with herd behavior and predator harvesting |
| Yong Yao,Jun He |
| Keywords:Leslie-Gower type system herd behavior predator harvesting Bogdanov-Takens bifurcation of codimension three degenerate Hopf bifurcation of codimension three |
| Abstract: |
| A Leslie-Gower type predator-prey system with herd behavior in prey and constant harvesting in predators is considered
in this paper. It is shown that there are two non-hyperbolic equilibria, one is
a nilpotent cusp of codimension at most three and the other one is a weak focus of multiplicity also at most three.
A complete analysis on bifurcations with codimension three is given as the bifurcation parameters vary, which includes
a Bogdanov-Takens bifurcation of codimension three and a degenerate Hopf bifurcation of codimension three.
The results indicate that the Leslie-Gower type system exhibits richer bifurcations than the classic Leslie-Gower system
and also reveal the complexity of the interaction between the prey, predators and humans. |
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