Phase Portraits, Hopf Bifurcations and Limit Cycles of the Ratio Dependent Holling-Tanner Models for Predator-prey Interactions - Sivakumar, M.; Balachandran, K. (Journal of Applied Nonlinear Dynamics, 2026)
In this paper we consider a ratio dependent Holling Tanner predator prey model with type II functional responses. We analyzed the local stability, phase portraits, existence and uniqueness of stable limit cycles and Hopf bifurcation. The ranges of the parameter involved are provided under which the unique interior equilibrium can be determined for a stable (or an unstable) node or focus without diffusion. Furthermore the Turing instability analysis of the system with diffusion are studied. Numerical simulations using MATLAB are carried out to demonstrate the theoretical results obtained.