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Coexistence and meta-coexistence for competing species. (English) Zbl 1034.35062

The dynamics of a family of competing species models where one of the species grows in the presence of finitely many refuges according to a logistic law is analyzed. Obtained results show how the model behaves like a superlinear indefinite problem for a single equation. As a result of the presence of refuges, for certain ranges of values of the parameters involved in the formulation of the model, the dynamics of its classical positive solutions is regulated by a metacoexistence state. (By it is meant a solution couple consisting of a metasolution coupled with a classical regular solution.)

MSC:

35K50 Systems of parabolic equations, boundary value problems (MSC2000)
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35B32 Bifurcations in context of PDEs
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