Bifurcation Behaviors Analysis on a Predator–Prey Model with Nonlinear Diffusion and Delay

Xu, Changjin; Li, Peiluan

doi:10.1007/s10883-013-9208-1

Cited by 5 publications

(2 citation statements)

References 20 publications

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“…Time delays have mainly been incorporated in the interaction part of the predator-prey models and not in the coupling terms, for instance see [11,12,13,14,15,16]. Abdllaoui et.…”

Section: Introductionmentioning

confidence: 99%

Rosenzweig-Macaurther Model with Holling type II Predator Functional Response for Constant Delayed Migration

Samuel

George

Kagendo

2019

ARJOM

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Predator-prey models describe the interaction between two species, the prey which serves as a food source to the predator. The migration of the prey for safety reasons after a predator attack and the predator in search of food, from a patch to another may not be instantaneous. In this paper, a Rosenzweig-MacAurther model with a Holling-type II predator functional response and time delay in the migration of both species is developed and analysed. Stability analysis of the system shows that depending on the prey growth and prey migration rates either both species go to extinction or co-exist. Numerical simulations show that a longer delay in the migration of the species leads makes the model to stabilize at a slower rate compared to when the delay is shorter. Relevant agencies likethe Kenya Wildlife Service should address factors that slow down migration of species, for example, destruction of natural habitats for human settlement and activities, which may cause delay in migration.

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“…Time delays have mainly been incorporated in the interaction part of the predator-prey models and not in the coupling terms, for instance see [11,12,13,14,15,16]. Abdllaoui et.…”

Section: Introductionmentioning

confidence: 99%

Rosenzweig-Macaurther Model with Holling type II Predator Functional Response for Constant Delayed Migration

Samuel

George

Kagendo

2019

ARJOM

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“…They are usually abundant in space with different densities at difference positions, and individuals have the natural tendency to move from areas of bigger population concentration to those of smaller population concentration to add the possibility of survival [9,[22][23][24][25][26][27]. For this reason, we consider the delayed stage-structure predator-prey system with homogeneous Neumann boundary condition, resulting from considering one spatial variable and incorporating diffusion terms to system (4).…”

mentioning

confidence: 99%

Stability and Hopf bifurcation in a reaction–diffusion predator–prey system with interval biological parameters and stage structure

Zhao

Wang

2014

Nonlinear Dyn

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This paper deals with a delayed reactiondiffusion predator-prey system combined with stage structure for prey and interval biological parameters. By taking the sum of delays as the bifurcation parameter, the local stability of the equilibrium points is investigated and the condition of Hopf bifurcation is obtained. In succession, using the normal form theory and the center manifold reduction for partial functional differential equations, we derive the explicit formulas determining stability, direction and other properties of bifurcating periodic solutions. Some numerical simulations are also included to illustrate our theoretical results.

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Stability and Hopf bifurcation analysis of a ratio-dependent predator–prey model with two time delays and Holling type III functional response

Wang

Peng

Liu

2015

Applied Mathematics and Computation

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Bifurcation Behaviors Analysis on a Predator–Prey Model with Nonlinear Diffusion and Delay

Cited by 5 publications

References 20 publications

Rosenzweig-Macaurther Model with Holling type II Predator Functional Response for Constant Delayed Migration

Rosenzweig-Macaurther Model with Holling type II Predator Functional Response for Constant Delayed Migration

Stability and Hopf bifurcation in a reaction–diffusion predator–prey system with interval biological parameters and stage structure

Stability and Hopf bifurcation analysis of a ratio-dependent predator–prey model with two time delays and Holling type III functional response

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