2018
DOI: 10.1186/s13662-018-1726-4
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Delay-induced Hopf bifurcation in a diffusive Holling–Tanner predator–prey model with ratio-dependent response and Smith growth

Abstract: In this paper, we study a diffusion Holling-Tanner predator-prey model with ratio-dependent functional response and Simth growth subject to a homogeneous Neumann boundary condition. Firstly, we use iteration technique and eigenvalue analysis to get the local stability and a Hopf bifurcation at the positive equilibrium. Secondly, by choosing the constant related to delay as bifurcation parameter we obtain periodic solutions near the positive equilibrium. Besides, by using center manifold theory and normal form … Show more

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