Spatial patterns through Turing instability in a reaction–diffusion predator–prey model

Lakshmi Narayan Guin

Mathematics and Computers in Simulation (MATCOM), 2015, vol. 109, issue C, 174-185

Abstract: Pattern formation in nonlinear complex systems is one of the central problems of the natural, social and technological sciences. In this paper, we consider a mathematical model of predator–prey interaction subject to self as well as cross-diffusion, arising in processes described by a system of reaction–diffusion equations (coupled to a system of ordinary differential equations) exhibiting diffusion-driven instability. Spatial patterns through Turing instability in a reaction–diffusion predator–prey model around the unique positive interior equilibrium of the model are discussed. Furthermore, we present numerical simulations of time evolution of patterns subject to self as well as cross-diffusion in the proposed spatial model and find that the model dynamics exhibits complex pattern replication in the two-dimensional space. The obtained results unveil that the effect of self as well as cross-diffusion plays an important role on the stationary pattern formation of the predator–prey model which concerns the influence of intra-species competition among predators.

Keywords: Reaction–diffusion systems; Self and cross-diffusion; Instability; Pattern formation (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475414002468
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:109:y:2015:i:c:p:174-185

DOI: 10.1016/j.matcom.2014.10.002

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().