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Mathematical Biosciences and Engineering

2019, Volume 16, Issue 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

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

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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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  • This article has been cited by:

    1. Xiaoni Wang, Gaihui Guo, Jian Li, Mengmeng Du, Qifeng Zhang, Qualitative Analysis of a Three-Species Reaction-Diffusion Model with Modified Leslie-Gower Scheme, 2021, 2021, 2314-8888, 1, 10.1155/2021/6650783
    2. Debasis Mukherjee, Dynamics of a diffusive two predators- one prey system , 2023, 1, 2980-2474, 47, 10.61383/ejam.20231349
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