Wang, Stability and Hopf bifurcation in a predator-prey model with the cost of anti-predator behaviors, Int. Yang, On uniqueness of limit cycles in general Bogdanov-Takens Bifurcation, Int. Chen, Stability and bifurcation in a Logistic model with Allee effect and feedback control, Int. Shao, Bifurcations of a prey-predator system with fear, refuge and additional food, Math. Turchin, Complex Population Dynamics: A Theoretical/Empirical Synthesis, Princeton University Press, 2003. Arditi, Credible, parsimonious and useful predator-prey models-A reply to Abrams, Gleeson, and Sarnelle, Ecology, 76 (1995), 1980–1985. Yuan, Dynamics of a stochastic predator-prey model with habitat complexity and prey aggregation, Ecol. Wang, Noise-induced transitions in a nonsmooth predator-prey model with stoichiometric constraints, Bull. Huang, Global dynamics of a ratio-dependent Holling-Tanner predator-prey system, J. Chen, Predator-prey systems in open advective heterogeneous environments with Holling-Tanner interaction term, J. Yuan, Pattern dynamic in a diffusive predator-prey model with hunting cooperations, Chaos Solitons Fract., 130 (2020), 109428. Bifurcation analysis in a Holling-Tanner predator-prey model with strong Allee effect. Moreover, numerical simulations are given to verify the theoretical results.Ĭitation: Yingzi Liu, Zhong Li, Mengxin He. The main conclusions of this paper complement and improve the previous paper. By verifying the transversality condition, we also prove that the system undergoes a Bogdanov-Takens bifurcation of codimension 2 or 3. We show that there exists bistable phenomena and two limit cycles.
By calculating the Lyapunov number, the system undergoes a subcritical Hopf bifurcation, supercritical Hopf bifurcation or degenerate Hopf bifurcation. As the values of parameters vary, we show that some bifurcations will appear in system. We confirm that the degenerate equilibrium of system can be a cusp of codimension 2 or 3.
In this paper, we analyze the bifurcation of a Holling-Tanner predator-prey model with strong Allee effect.
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