Eur. Phys. J. Plus (2019) 134: 574
https://doi.org/10.1140/epjp/i2019-12920-7

Regular Article

Spatiotemporal dynamics of reaction-diffusion equations modeling predator-prey interactions using DUNE-PDELab

¹ Department of Mathematics, COMSATS University, Park Road Chak Shahzad, Islamabad, Pakistan
² Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Hasa, Saudi Arabia

^* e-mail: ishtiaqali@comsats.edu.pk

Received: 16 May 2019
Accepted: 6 August 2019
Published online: 15 November 2019

Abstract

Reaction-diffusion systems (RDS) help us to understand the distribution of the concentration of substances in space or time under the influence of two phenomena: local chemical reactions where the substances are transmuted into one another, and diffusion which causes the substances to spread out over a surface in space. Analytical solutions for these behavioral models are still lacking, therefore it is essential to use some numerical methods to find approximate solution to these systems as the numerical results will allow us the use of parameters fitting. This study focuses on the numerical approximation based on finite-element scheme together with the powerful DUNE-PDELab package to investigate the spatio-temporal dynamics of the structure of predator-prey diffusive model. The scheme is introduced for approximation of predator-prey with Holling type-II functional response, while the growth is logistic, subject to some appropriate initial and boundary conditions. The simulations were obtained in the two-dimensional case, which demonstrate that the initial and boundary conditions play an important role in identifying the spatio-temporal dynamics of predator-prey interactions.