The Bifurcation analysis of Prey-Predator Model in The Presence of Stage Structured with Harvesting and Toxicity

For a mathematical model the local bifurcation like pitchfork, transcritical and saddle node occurrence condition is defined in this paper. With the existing of toxicity and harvesting in predator and prey it consist of stage-structured. Near the positive equilibrium point of mathematical model on the Hopf bifurcation with particular emphasis it established. Near the equilibrium point E₀ the transcritical bifurcation occurs it is described with analysis. And it shown that at equilibrium points E₁ and E₂ happened the occurrence of saddle-node bifurcation. At each point the pitch fork bifurcation occurrence is not happened. For the occurrence of local bifurcation illustration there used some numerical simulation.