In this paper we revisit a discrete predator-prey model with Holling Ⅳ functional response. By using the method of semidiscretization, we obtain new discrete version of this predator-prey model. Some new results, besides its stability of all fixed points and the transcritical bifurcation, mainly for codimension two 1:1 strong resonance bifurcation, are derived by using the center manifold theorem and bifurcation theory, showing that this system possesses complicate dynamical properties.
Citation: Mianjian Ruan, Chang Li, Xianyi Li. Codimension two 1:1 strong resonance bifurcation in a discrete predator-prey model with Holling Ⅳ functional response[J]. AIMS Mathematics, 2022, 7(2): 3150-3168. doi: 10.3934/math.2022174
In this paper we revisit a discrete predator-prey model with Holling Ⅳ functional response. By using the method of semidiscretization, we obtain new discrete version of this predator-prey model. Some new results, besides its stability of all fixed points and the transcritical bifurcation, mainly for codimension two 1:1 strong resonance bifurcation, are derived by using the center manifold theorem and bifurcation theory, showing that this system possesses complicate dynamical properties.
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Mianjian Ruan, Chang Li, Xianyi Li. Codimension two 1:1 strong resonance bifurcation in a discrete predator-prey model with Holling Ⅳ functional response[J]. AIMS Mathematics, 2022, 7(2): 3150-3168. doi: 10.3934/math.2022174
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