WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 14, 2015
Periodic Solutions for Three-Species Diffusive Systems with Beddington-Deangelis and Holling-Type Iii Schemes
Authors: , , ,
Abstract: This paper is concerned with the three-species diffusive systems in a periodic environment, which arises in a one-prey and two-competing-predator population model with Beddington-Deangelis and Holling-type III schemes. By using eigenvalue analysis, bifurcation theories and Schauder estimates, the existence of positive periodic solutions of the single prey species system, two-species predator-prey systems with different functional responses and three-species periodic diffusive systems are investigated. The necessary and sufficient conditions are described by the principal eigenvalue of the periodic parabolic operators. Furthermore, the alternative sufficient conditions characterised by the integral form of the parameters of the systems are more convenient to the biological explanation
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Keywords: Positive periodic solutions, principal eigenvalue, Schauder estimates, global bifurcation, decoupling
Pages: 47-56
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 14, 2015, Art. #5