Emergent impacts of quadratic mortality on pattern formation in a predator–prey system

Ghorai, Santu; Poria, Swarup

doi:10.1007/s11071-016-3222-2

Cited by 21 publications

(4 citation statements)

References 43 publications

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“…In fact, a type of quadratic mortality was also considered, that is, we modified the term −Dv to −Dv 2 . Ghorai and Poria [12] considered the effects of a diffusive predator-prey system with quadratic mortality rate and Holling II type. And Yuan et al [13] investigated the following diffusive model:…”

Section: Historymentioning

confidence: 99%

Turing instability in a diffusive predator-prey model with multiple Allee effect and herd behavior

Xiao¹,

Xia²

2023

Preprint

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Diffusion-driven instability and bifurcation analysis are studied in a predator-prey model with herd behavior and quadratic mortality by incorporating multiple Allee effect into prey species.The existence and stability of the equilibria of the system are studied. The sufficient and necessary conditions for Turing instability occurring are obtained. And the stability and direction of Hopf and steady state bifurcations are explored by using the normal form method. Furthermore, some numerical simulations are presented to support our theoretical analysis. We found that too large diffusion rate of prey prevents Turing instability from emerging. The biomass conversion rate does affect the stability of the system and the occurrence of Turing instability. This indicates that the biomass conversion rate is essentially significant for the predator-prey system. Finally, we summarize our findings in the conclusion.

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Section: Historymentioning

confidence: 99%

Turing instability in a diffusive predator-prey model with multiple Allee effect and herd behavior

Xiao¹,

Xia²

2023

Preprint

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“…The study of weakly nonlinear analysis helps to understand the etymology of amplitude equations. In this section we derive amplitude equations with the help of the standard multiple-scale analysis [52,66,70,18]. Let us assume that the Turing patterns [61] have three pairs of modes (k i , -k i , i = 1, 2, 3) making an angle of 2π 3 between each pair with the following conditions |k i | = κ T and 3 i=1 k i = 0.…”

Section: Weakly Nonlinear Analysismentioning

confidence: 99%

“…It is a well known fact that the Turing pattern formations near the bifurcation threshold parameter are described by amplitude equations [18]. However if the bifurcation parameter is far away from the bifurcation threshold parameter, amplitude equations fail to explain the pattern phenomena.…”

Section: Spatio-temporal Patterns In Two Spatial Dimensionsmentioning

confidence: 99%

Self-diffusion Driven Pattern Formation in Prey-Predator System with Complex Habitat under Fear Effect

Jana

Batabyal

Lakshmanan

2020

Preprint

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In the present work, we explore the influence of habitat complexity on the activities of prey and predator of a spatio-temporal system by incorporating self diffusion. First we modify the Rosenzweig-MacArthur predator-prey model by incorporating the effects of habitat complexity on the carrying capacity and fear effect of prey and predator functional response. We establish conditions for the existence and stability of all feasible equilibrium points of the non-spatial model and later we prove the existence of Hopf and transcritical bifurcations in different parametric phase-planes analytically and numerically. The stability of the spatial system is studied and we discuss the conditions for Turing instability. Selecting suitable control parameter from the Turing space, the existence conditions for stable patterns are derived using the amplitude equations. Results obtained from theoretical analysis of the amplitude equations are justified by numerical simulation results near the critical parameter value. Further, from numerical simulation, we illustrate the effect of diffusion of the dynamical system in the spatial domain by different pattern formations. Thus our model clearly shows that the fear effect of prey and predator's functional response make an anti-predator behaviour including habitat complexity which helps the prey to survive in the spatio-temporal domain through diffusive process.

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“…Based on this consideration, for the Gause-type predator-prey system, Ko et al [14] studied the existence/non-existence of non-constant positive solutions, the asymptotic behavior of spatially inhomogeneous solutions and the local existence of periodic solutions, and Liu et al [15] proved the existence of a unique globally stable periodic solution. Further considering the quadratic mortality is suitable for intermediate predators, some scholars [16][17][18][19] have introduced the quadratic mortality into the predator-prey system to analysis. In in most real ecological systems, one biological population does not respond immediately to the interactions of populations of other species.…”

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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Emergent impacts of quadratic mortality on pattern formation in a predator–prey system

Cited by 21 publications

References 43 publications

Turing instability in a diffusive predator-prey model with multiple Allee effect and herd behavior

Turing instability in a diffusive predator-prey model with multiple Allee effect and herd behavior

Self-diffusion Driven Pattern Formation in Prey-Predator System with Complex Habitat under Fear Effect

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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