Stability and Hopf bifurcation of a delayed-diffusive predator–prey model with hyperbolic mortality and nonlinear prey harvesting

Zhang, Fengrong; Li, Yan

doi:10.1007/s11071-016-3318-8

Cited by 21 publications

(5 citation statements)

References 36 publications

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“…Overall, it is found that a weak Allee effect, fear effect, and delay all play significant roles in population dynamics. e previous studies show that the Allee effect and delay can induce Hopf bifurcation and that the fear effect will promote the system stability [4,22,42,43]. Wang et al [11] considered the fear effect term in the interacting prey-predator model and completed a comprehensive work on fear factor.…”

Section: Discussionmentioning

confidence: 99%

Population Dynamic Study of Prey‐Predator Interactions with Weak Allee Effect, Fear Effect, and Delay

Hua

Wei

et al. 2022

Journal of Mathematics

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In this study, a predator-prey model with the Allee effect and fear effect is established. We use the comparison principle to prove boundedness. The zero equilibrium point and nonzero equilibrium point of the model are calculated, and the local stability conditions are obtained. Next, according to the Sotomayor theorem, the cross-sectional conditions of transcritical bifurcation and Hopf bifurcation are obtained. The conditions for the Hopf bifurcation to be supercritical or subcritical can be calculated by the normal form theory. Then, to make the model more realistic, we introduce the gestation delay in the proposed mathematical model. Stability and Hopf bifurcation are also analyzed. Finally, several numerical simulations are presented to verify the conclusions. Our results demonstrate that the Allee effect, fear effect, and delay play significant roles in population dynamics. The Allee effect and delay destabilize the originally stable model, after which Hopf bifurcation occurs. However, the fear effect can enhance stable coexistence.

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Section: Discussionmentioning

confidence: 99%

Population Dynamic Study of Prey‐Predator Interactions with Weak Allee Effect, Fear Effect, and Delay

Hua

Wei

et al. 2022

Journal of Mathematics

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“…Delay is prevalent in population systems, for instance, predators may experience gestational delay after consuming prey. Delay reflects inherent population characteristics [10][11][12][13][14]. In comparison to population systems without delay, delayed population systems can exhibit more complex nonlinear dynamical behaviors [15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Stability and Bifurcation Control for a Generalized Delayed Fractional Food Chain Model

Li,

Liu,

Zhao

et al. 2024

Fractal Fract

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In this paper, a generalized fractional three-species food chain model with delay is investigated. First, the existence of a positive equilibrium is discussed, and the sufficient conditions for global asymptotic stability are given. Second, through selecting the delay as the bifurcation parameter, we obtain the sufficient condition for this non-control system to generate Hopf bifurcation. Then, a nonlinear delayed feedback controller is skillfully applied to govern the system’s Hopf bifurcation. The results indicate that adjusting the control intensity or the control target’s age can effectively govern the bifurcation dynamics behavior of this system. Last, through application examples and numerical simulations, we confirm the validity and feasibility of the theoretical results, and find that the control strategy is also applicable to eco-epidemiological systems.

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“…In in most real ecological systems, one biological population does not respond immediately to the interactions of populations of other species. Considering that the reproduction of predator after predating the prey is not instantaneous but will be mediated by some discrete time delay required for gestation of the predator, many scholars have incorporated the gestation time of predator into the predator-prey system, and studied the stability of equilibrium, Hopf bifurcation, Bogdanov-Takens bifurcation and so on, see [20][21][22][23][24]. The time delay may greatly affect the dynamic behavior of biological systems, so we suppose that the gestation time τ > 0 of predator occurs in the predator response term.…”

Section: Introductionmentioning

confidence: 99%

Global Hopf Bifurcation Of a Delayed Diffusive Gause-Type Predator-Prey System with the Fear Effect and Holling Type III Functional Response

Zhang,

Liu,

2024

Math. Model. Nat. Phenom.

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In this paper, a delayed diffusive predator-prey system with the fear effect and Holling type III functional response is considered, and Neumann boundary condition is imposed on this system. First, we explore the stability of the unique positive constant steady state and the existence of local Hopf bifurcation. Then the global attraction domain G∗ of system (4) is obtained by the comparison principle and the iterative method. Through constructing the Lyapunov function, we investigate uniform boundedness of periodic solutions’periods. Finally, we prove the global continuation of periodic solutions by the global Hopf bifurcation theorem of Wu. Moreover, some numerical simulations that support the analysis results are given.

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Stability and Hopf bifurcation of a delayed-diffusive predator–prey model with hyperbolic mortality and nonlinear prey harvesting

Cited by 21 publications

References 36 publications

Population Dynamic Study of Prey‐Predator Interactions with Weak Allee Effect, Fear Effect, and Delay

Population Dynamic Study of Prey‐Predator Interactions with Weak Allee Effect, Fear Effect, and Delay

Stability and Bifurcation Control for a Generalized Delayed Fractional Food Chain Model

Global Hopf Bifurcation Of a Delayed Diffusive Gause-Type Predator-Prey System with the Fear Effect and Holling Type III Functional Response

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