Mathematical Biosciences and Engineering, 2019, 16(5): 3988-4006. doi: 10.3934/mbe.2019197

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

Dongfu Tong, Yongli Cai, Bingxian Wang, Weiming Wang

School of Mathematical Science, Huaiyin Normal University, Huaian, 223300, P.R. China

Received: , Accepted: , Published:

Special Issues: Differential Equations in Mathematical Biology

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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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