Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a prey refuge

By Wonlyul Ko, Kimun Ryu. 2006

275 citations recorded by the source corpus.

We study a predator–prey model with Holling type II functional response incorporating a prey refuge under homogeneous Neumann boundary condition. We show the existence and non-existence of non-constant positive steady-state solutions depending on the constant m∈(0,1], which provides a condition for protecting (1−m)u of prey u from predation. Moreover, we investigate the asymptotic behavior of spacially inhomogeneous solutions and the local existence of periodic solutions.

Subfields: Applied Mathematics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/0f2c1e7d1988b400ac2fd5b69365dd6b88ce8cc0

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Citations in the corpus

A Leslie-Gower predator-prey model with disease in prey incorporating a prey refuge (2015, background): “Some of the researchers [7,27,29,39,55] have investigated the influence of prey refuge and concluded that the refuge used by the prey has a stabilizing effect on the predator–prey interaction and also that the prey species can be prevented well from extinction by using such policy.”
Dynamics and pattern formation in a diffusive predator–prey system with strong Allee effect in prey (2011, unknown): “1) has been considered in many articles, see for example [11,13, 19,25,28,60].”
Stability, Steady‐State Bifurcations, and Turing Patterns in a Predator–Prey Model with Herd Behavior and Prey‐taxis (2017, methodology): “Proof: Using the first equation of (16) and the maximum principle in [45], we obtain u ≤ 1.”
Non-existence of non-constant positive steady states of two Holling type-II predator–prey systems: Strong interaction case (2009, background): “It was proved in [18,41] that (k,0) is globally asymptotically stable when λ k, and (λ, vλ) is globally asymptotically stable when λ ∈ [k−1,k).”
Global bifurcation of solutions for a predator–prey model with prey‐taxis (2015, unknown): “0, K0/ is globally asymptotically stable [7].”
Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system ✩ (2009, background): “When λ k (or 0 < m < θ(1 + k)/k), it is well known that (k,0) is globally asymptotically stable (see for example [13,27]).”
Global bifurcation analysis and pattern formation in homogeneous diffusive predator–prey systems (2016, background): “Ko and Ryu [21] obtained some results on the global stability of the equilibrium solution for certain parameter ranges.”
Global analysis of a Holling type II predator–prey model with a constant prey refuge (2014, background): “Recently, Holling type II predator–prey models with a refuge have been investigated by many authors [4, 11, 16, 22, 26, 27, 29].”