Stability analysis in prey–predator system with mixed functional response

Abstract

Purpose

This paper aims to propose and analyse a two-prey–one-predator system with mixed functional response.

Design/methodology/approach

The predator exhibits Holling type IV functional response to one prey and Holling type I response to other. The occurrence of various positive equilibrium points with feasibility conditions are determined. The local and global stability of interior equilibrium points are examined. The boundedness of system is analysed. The sufficient conditions for persistence of the system is obtained by using Bendixson–Dulac criteria. Numerical simulations are carried out to illustrate the analytical findings.

Findings

The authors have derived the local and global stability condition of interior equilibrium of the system.

Originality/value

The authors observe that the critical values of some system parameter undergo Hopf bifurcation around some selective equilibrium. Hence, numerical simulations reveal the condition for the system to be stable and oscillatory.

Citation

Madhusudanan, V. and Vijaya, S. (2016), "Stability analysis in prey–predator system with mixed functional response", World Journal of Engineering, Vol. 13 No. 4, pp. 364-369. https://doi.org/10.1108/WJE-08-2016-048