### Mathematical Biosciences and Engineering

2019, Issue 5: 3988-4006. doi: 10.3934/mbe.2019197
Research article Special Issues

# Bifurcation structure of nonconstant positive steady states for a diffusive predator-prey model

• Received: 31 January 2019 Accepted: 18 April 2019 Published: 06 May 2019
• In this paper, we make a detailed descriptions for the local and global bifurcation structure of nonconstant positive steady states of a modified Holling-Tanner predator-prey system under homogeneous Neumann boundary condition. We first give the stability of constant steady state solution to the model, and show that the system exhibits Turing instability. Second, we establish the local structure of the steady states bifurcating from double eigenvalues by the techniques of space decomposition and implicit function theorem. It is shown that under certain conditions, the local bifurcation can be extended to the global bifurcation.

Citation: Dongfu Tong, Yongli Cai, Bingxian Wang, Weiming Wang. Bifurcation structure of nonconstant positive steady states for a diffusive predator-prey model[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 3988-4006. doi: 10.3934/mbe.2019197

### Related Papers:

• In this paper, we make a detailed descriptions for the local and global bifurcation structure of nonconstant positive steady states of a modified Holling-Tanner predator-prey system under homogeneous Neumann boundary condition. We first give the stability of constant steady state solution to the model, and show that the system exhibits Turing instability. Second, we establish the local structure of the steady states bifurcating from double eigenvalues by the techniques of space decomposition and implicit function theorem. It is shown that under certain conditions, the local bifurcation can be extended to the global bifurcation.

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