Stability and bifurcation in a diffusive prey-predator system. Nonlinear bifurcation analysis. (Q1847584)

A predator-prey model with nonlinear prey growth and Lotka-Volterra type functional response is considered. Due to the nonlinearity the system undergoes a Hopf bifurcation at the positive steady state when the death rate of the predator passes a critical value. The authors then studied the effect of small inhomogeneous perturbation on this bifurcation value and derived a new bifurcation value which depends on the diffusion coefficient ratio and indicates the well-known Turing instability phenomenon.