Extinction and coexistence of competing prey species in ecological systems

Article type: Research Article

Authors: Upadhyay, Ranjit Kumar^{a; *} | Iyengar, S.R.K.^{b; 1}

Affiliations: [a] Department of Applied Mathematics, Indian School of Mines, Dhanbad, Jharkhand, 826 004, India | [b] Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi, 110 016, India

Correspondence: [*] Corresponding author.

Note: [1] Dedicated to Prof. M.K. Jain who was my teacher and colleague.

Abstract: In this paper, a Gause type mathematical model is proposed to study the effect of predation on two competing prey species in which the predator species is influenced by the damage effect caused by crowding from the members of its own population in a diffusive system. In the absence of diffusion, criteria for local stability, instability and global stability of the non-negative equilibria of the system has been obtained. Conditions for the coexistence of the two competing prey species and the extinction of either of the prey are tested numerically. These numerical simulations suggest that there exists a stable limit cycle in some ranges of the parameters and extinction of the prey species in some other ranges of the parameters. Basin boundary calculations indicate the coexistence of different attractors on the same set of parametric values.

DOI: 10.3233/JCM-2006-61-411

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 6, no. 1-4, pp. 131-150, 2006