Article Contents
Article Contents

# Dynamics of a stage structure prey-predator model with ratio-dependent functional response and anti-predator behavior of adult prey

• In this paper, a predator-prey interaction model among juvenile prey, adult prey and predator has been developed where stage structure is considered on prey species. The functional responses has been considered as ratio dependent. It is assumed that that the adult prey is strong enough such that it has an anti-predator characteristic. Global dynamics of the co-existing equilibrium point has been discussed with the help of the geometric approach. Furthermore, it is established that the proposed system undergoes through a Hopf bifurcation with respect to some important parameters. Finally, some numerical simulations have been done to test our theoretical results.

Mathematics Subject Classification: Primary: 92B05, 92D25; Secondary: 92D40.

 Citation:

• Figure 1.  Local stability of the equilibrium point $E_1$

Figure 2.  Local stability of the equilibrium point $E^{*}$

Figure 3.  Global stability of interior equilibrium

Figure 4.  Bifurcation diagram of system $(1)$ with respect to $\eta$

Figure 5.  Bifurcation diagram of system $(1)$ with respect to $\beta$

Figure 6.  Bifurcation diagram of system $(1)$ with respect to $\beta_1$

Figure 7.  Bifurcation diagram of system $(1)$ with respect to $\beta_2$

Figure 8.  Bifurcation diagram of system $(1)$ with respect to $\gamma$

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