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Abstract
In this work, we analyze a two-dimensional continuous-time differential equations system derived from a Leslie–Gower predator–prey model with a generalist predator and prey group defence. For our model, we fully characterize the existence and quantity of equilibrium points in terms of the parameters, and we use this to provide necessary and sufficient conditions for the existence and the explicit form of two kinds of equilibrium points: both a degenerate one with associated nilpotent Jacobian matrix, and a weak focus. These conditions allows us to determine whether the system undergoes Bogdanov–Takens and Hopf bifurcations. Consequently, we establish the existence of a simultaneous Bogdanov–Taken and Hopf bifurcation. With this double bifurcation, we guarantee the existence of a new Hopf bifurcation curve and two limit cycles on the system: an infinitesimal and another non-infinitesimal.
Original language | English |
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Article number | 255 |
Journal | Qualitative Theory of Dynamical Systems |
Volume | 23 |
Issue number | Suppl 1 |
DOIs | |
State | Published - Nov 2024 |
Bibliographical note
Publisher Copyright:© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.
Keywords
- Bogdanov–Takens bifurcation
- Hopf bifurcation
- Non-monotonic functional response
- Predator–prey model
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Simultaneous Hopf and Bogdanov-Takens bifurcations on a Leslie-Gower type model
Puchuri, L. (Author), Bueno Tangoa, O. M. (Author), Gonzalez-Olivares, E. (Author) & Rojas-Palma, A. (Author)
9 Nov 2023Activity: Unpublished and/or developing manuscripts › Manuscripts sent to indexed journals or publishers