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Zbl 1202.35115
Lin, Zhigui; Liu, Jiahong; Pedersen, Michael
Periodicity and blowup in a two-species cooperating model. (English)
[J] Nonlinear Anal., Real World Appl. 12, No. 1, 479-486 (2011). ISSN 1468-1218

Summary: The cooperating two-species Lotka-Volterra model is discussed. Existence and asymptotic behavior of $T$-periodic solutions for a periodic reaction diffusion system under homogeneous Dirichlet boundary conditions are first investigated. The blowup properties of solutions for the same system are given then. It is shown that periodic solutions exist if the intra-specific competitions are strong whereas blowup solutions exist under certain conditions if the intra-specific competitions are weak. Numerical simulations and a brief discussion are also presented in the last section.

MSC 2000:: *35K51
92D25 Population dynamics
35K57 Reaction-diffusion equations
35B10 Periodic solutions of PDE
35K58
35B44

Keywords: upper and lower solutions; intra-specific competitions; Dirichlet boundary conditions

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