Bifurcation analysis of continuous and discrete time predator-prey models with habitat complexity

This paper investigates a predator-prey model with a Holling Type II functional response in the presence of habitat complexity. The model is formulated in continuous time and discretized using the forward Euler scheme to obtain its discrete counterpart. Fundamental dynamical properties, including positivity, boundedness, equilibrium existence, and local stability, are established for both systems. The dynamical behavior of the continuous model is further explored through Hopf and transcritical bifurcation analyses, whereas Neimark-Sacker bifurcation is investigated in the discrete framework. In addition, Turing instability analysis is performed for the reaction-diffusion system. Finally, numerical simulations are presented to validate the theoretical results.