the bifurcation analysis of an eco-toxicant model with anti-predator behavior

In this study, the mathematical model of four differential equations for organisms that describe the effect of anti-predation behavior, age stage and toxicity have been analyzed. local bifurcation and hopf bifurcation have been studied by changing a parameter of a model to study the dynamic behavior determined by bifurcation curves and the occurrence states of bifurcation saddle node, transcritical and pitch fork bifurcation. the potential equilibrium point at which hopf bifurcation occurs has been determined and the results of the bifurcation behavior analysis have been fully presented using numerical simulation.