Allee effect and bistability in a spatially heterogeneous predator-prey model
By Yihong Du, Junping Shi. 2007
138 citations recorded by the source corpus.
A spatially heterogeneous reaction-diffusion system modelling predator-prey interaction is studied, where the interaction is governed by a Holling type II functional response. Existence of multiple positive steady states and global bifurcation branches are examined as well as related dynamical behavior. It is found that while the predator population is not far from a constant level, the prey population could be extinguished, persist or blow up depending on the initial population distributions, the various parameters in the system, and the heterogeneous environment. In particular, our results show that when the prey growth is strong, the spatial heterogeneity of the environment can play a dominant role for the presence of the Allee effect. Our mathematical analysis relies on bifurcation theory, topological methods, various comparison principles and elliptic estimates. We combine these methods with monotonicity arguments to the system through the use of some new auxiliary scalar equations, though the system itself does not keep an order structure as the competition system does. Among other things, this allows us to obtain partial descriptions of the dynamical behavior of the system.
Subfields: Computer Networks and Communications, Modeling and Simulation, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/6f71c38b3dea1f36323e00b8e81f63bf9e6e31b8
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In Computer Networks and Communications
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Citations in the corpus
- Effect of a protection zone in the diffusive Leslie predator-prey model (2009, background): “Very recently, some efforts have been devoted to addressing this problem, and certain effects of heterogeneity of the environment on some competition and predator–prey models have been revealed; see, for example, [3,5–9,11,18,19,25–27,31,33,34].”
- Dynamics of a host-pathogen system on a bounded spatial domain (2015, unknown): “[10, 11]): α′(0) = − 〈l, F(u,w),(u,w)(α, u1, 0)[φ0, ψ0](2)〉 2〈l, Fα,(u,w)(α, u1, 0)[φ0, ψ0]〉 ,”
- Non-existence of non-constant positive steady states of two Holling type-II predator–prey systems: Strong interaction case (2009, background): “On the other hand, it is known that spatial heterogeneity may induce complex spatiotemporal patterns [6,7].”
- 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]).”
- Local dynamics of a diffusive predator–prey model in spatially heterogeneous environment (2017, methodology): “We refer to [7, 23, 24, 25, 26] for surveys of recent development on the effects of dispersal and spatial heterogeneity on population dynamics; See [2, 11, 21, 18] for single species models, [9, 10, 12, 13, 14, 27] for predator-prey models, and [15, 16, 17, 19, 20] for competition models.”
- On global bifurcation for quasilinear elliptic systems on bounded domains (2009, background): “The bifurcation analysis for A′ is essentially the same as A, details can be found in, for example, [8,13].”
- A diffusive predator–prey model with a protection zone☆ (2006, background): “Our results in this section are qualitatively similar to those in Section 3 of our earlier work [24], where no protection zone is present.”
- 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].”