Dynamical analysis in a diffusive predator-prey model with ratio-dependent functional response
The spatiotemporal dynamics of a predator-prey model with ratio-dependent functional responses has been studied.To explore the joint effect of prey growth rate and the ratio of diffusion coefficients on the dynamics of the system,the following analyses are performed,including the stability analysis of constant steady states;sufficient conditions for the occurrence of Hopf bifurcation,Turing bifurcation,and Turing-Hopf bifurcation;the derivation and calculation of the normal form near the Turing-Hopf singularity.The results demonstrate that the small change in prey growth rate and the ratio of diffusion coefficients can destabilize the constant steady states,and lead to the complex spatiotemporal behaviors,including spatially homogeneous and spatially inhomogeneous periodic solutions,and non-constant steady states solutions.The numerical simulations to demonstrate the theoretical analysis are provided,and the numerical simulations coincide with our theoretical results.
Turing-Hopf bifurcationHopf bifurcationratio-dependentpredator-prey model
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