Bifurcation analysis of a plant-herbivore model with toxin-determined functional response (Q932277)

The authors study the dynamics of the system \[ \begin{aligned}\frac{dN}{dt}&=rN(1- {N}/{K})-C(N)P,\\ \frac{dP}{dt}&=BC(N)P-dP, \end{aligned} \] where \(C(N)=f(N)(1-f(N)/(4G)\) and \(f(N)\) is the Holling Type II functional response by explicitly including a reduction in the consumption of plants by the herbivore due to chemical defenses. A detailed bifurcation analysis of the system reveals a rich array of possible behaviors including cyclical dynamics through Hopf bifurcations and homoclinic bifurcation. The results are obtained not only analytically but also confirmed and extended numerically.