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Periodicity and blowup in a two-species cooperating model. (English) Zbl 1202.35115
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:
 35K51 Second-order parabolic systems, initial bondary value problems 92D25 Population dynamics (general) 35K57 Reaction-diffusion equations 35B10 Periodic solutions of PDE 35K58 Semilinear parabolic equations 35B44 Blow-up (PDE)
##### References:
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