Dynamics Behaviors of a Reaction-Diffusion Predator-Prey System with Beddington-DeAngelis Functional Response and Delay

Du, Peng; Duan, Caixia; Liao, Xinyuan

doi:10.4236/am.2014.56080

Cited by 4 publications

(1 citation statement)

References 15 publications

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“…Although in several cases, diffusion has not given proper answers to questions about species propagation (Higgins & Richardson, 1996), it is still useful to understand the richness of the interaction between populations. For example, reaction-diffusion systems have made possible an understanding of the onset of spatial oscillations in predator-prey models (Ma & Li, 2013), the dynamics of propagating waves (Du, Duan, & Liao, 2014), and formation of spatial patterns in the medium (Hu, Li, & Wang, 2015;Murray, 2007;Sun, Jin, Liu, & Li, 2008).…”

Section: Introductionmentioning

confidence: 99%

Diffusion as a strategy for survival in an invasion predator–prey model

Olmos‐Liceaga¹,

Villavicencio-Pulido

Acuña‐Zegarra³

2017

Natural Resource Modeling

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In some ecosystems, the invasion of species may lead to extinction or displacement of the local species that are in the medium. In this work, we present a theoretical predator–prey model based on reaction diffusion equations, where each species has a strong Allee effect. We use the diffusion coefficients as parameters in a one‐dimensional environment to show that prey can either survive or become extinct from its habitat. When the results are extended to two spatial dimensions, diffusion alone is no longer a sufficient condition in order to assure extinction or survival of the prey species; in this case, the geometry of the propagation front plays an essential role in the dynamics. Finally, a discussion about strategies for survival and extinction of the prey species is considered. The results can be useful in understanding invasion for species such as the Argentine ant Linepithema humile or to help to find control strategies for unwanted species in an ecosystem by introducing a predator.

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