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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.
35K51Second-order parabolic systems, initial bondary value problems
92D25Population dynamics (general)
35K57Reaction-diffusion equations
35B10Periodic solutions of PDE
35K58Semilinear parabolic equations
35B44Blow-up (PDE)
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