Hopf bifurcation and stability in a Beddington-DeAngelis predator-prey model with stage structure for predator and time delay incorporating prey refuge

Xiao, Zaowang; Li, Zhong; Zhu, Zhenliang; Chen, Fengde

doi:10.1515/math-2019-0014

Cited by 33 publications

(10 citation statements)

References 23 publications

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“…In researching the dynamic behaviors of the predator-prey model, some scholars [2,[10][11][12][17][18][19][20] considered the impact of the functional response for the predator-prey. For example, Yu [18] studied the global asymptotic stability of a predator-prey model with modified Leslie-Gower and Holling-type II schemes:…”

Section: Introductionmentioning

confidence: 99%

Dynamic behaviors of Lotka–Volterra predator–prey model incorporating predator cannibalism

et al. 2019

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A Lotka-Volterra predator-prey model incorporating predator cannibalism is proposed and studied in this paper. The existence and stability of all possible equilibria of the system are investigated. Our study shows that cannibalism has both positive and negative effect on the stability of the system, it depends on the dynamic behaviors of the original system. If the predator species in the system without cannibalism is extinct, then suitable cannibalism may lead to the coexistence of both species, in this case, cannibalism stabilizes the system. If the cannibalism rate is large enough, the prey species maybe driven to extinction, while the predator species are permanent. If the two species coexist in the stable state in the original system, then predator cannibalism may lead to the extinction of the prey species. In this case, cannibalism has an unstable effect. Numeric simulations support our findings.

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Section: Introductionmentioning

confidence: 99%

Dynamic behaviors of Lotka–Volterra predator–prey model incorporating predator cannibalism

et al. 2019

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“…Obviously, one could not prove this conjecture by directly applying the method of [39,40]. By developing the analysis technique of Wu et al [13], we finally give a strict proof of Theorem 1.1. Obviously, Theorem 1.1 essentially improves the main result of [39] since our condition is cannibalism independent, which means that if the original system is permanent, then cannibalism has no influence on the persistence property of the system.…”

Section: Resultsmentioning

confidence: 93%

Note on the persistence and stability property of a stage-structured prey–predator model with cannibalism and constant attacking rate

et al. 2020

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We revisit the persistence and stability property of a stage-structured prey-predator model with cannibalism and constant attacking rate. By using the differential inequality theory and Bendixson-Dulac criterion, we show that if the system without cannibalism is permanent, then the system with cannibalism is also permanent. By developing some new analysis technique, we obtain a new set of sufficient conditions which ensure the global asymptotic stability of the nonnegative equilibrium, which means that, under some suitable assumption, prey cannibalism has no influence on the stability property of the predator free equilibrium. Our results essentially improve the corresponding results of Limin Zhang and Chaofeng Zhang.

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“…Xiao et al [41] studied the following Beddington-DeAngelis prey-predator model with stage structure and prey refuge…”

Section: Model Descriptionmentioning

confidence: 99%

Hopf Bifurcation and Control of a Fractional-Order Delay Stage Structure Prey-Predator Model with Two Fear Effects and Prey Refuge

2022

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A generalized delay stage structure prey-predator model with fear effect and prey refuge is considered in this paper via introducing fractional-order and fear effect induced by immature predators. Hopf bifurcation and control of this system are investigated though regarding the delay as the parameter. Firstly, by using the method of linearization and Laplace transform, the roots of the characteristic equation of the linearized system of the original system are discussed, and the sufficient conditions for the system exhibits an unstable state of symmetrical periodic oscillation (Hopf bifurcation) are explored. Secondly, a linear delay feedback controller is added to the system to increase the stability domain successfully. Thirdly, numerical simulations are performed to validate the theoretical analysis, and the various impacts on the dynamical behavior of the system occurring by fear effects, prey refuge, and each fractional-order are illustrated, respectively. Furthermore, the influence of feedback gain on the bifurcation critical point is analyzed. Finally, an analysis based on the results and in-depth research about this system under the biological background is stated in the conclusion.

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Hopf bifurcation and stability in a Beddington-DeAngelis predator-prey model with stage structure for predator and time delay incorporating prey refuge

Cited by 33 publications

References 23 publications

Dynamic behaviors of Lotka–Volterra predator–prey model incorporating predator cannibalism

Dynamic behaviors of Lotka–Volterra predator–prey model incorporating predator cannibalism

Note on the persistence and stability property of a stage-structured prey–predator model with cannibalism and constant attacking rate

Hopf Bifurcation and Control of a Fractional-Order Delay Stage Structure Prey-Predator Model with Two Fear Effects and Prey Refuge

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