Positive solutions for a modified Leslie–Gower prey–predator model with Crowley–Martin functional responses

Abstract

In this paper, we study a modified Leslie–Gower prey–predator model with Crowley–Martin functional response. The stability and instability of the trivial and semi-trivial solutions was studied by analyzing the eigenvalues of the linearized system. The existence, multiplicity and uniqueness of positive steady state solutions were shown by using bifurcation theory, degree theory, energy estimate and asymptotic behavior analysis. Furthermore, all results were characterized in parameter plane.