Global Behavior for a Strongly Coupled Predator-Prey Model with One Resource and Two Consumers | Zendy

Yujuan Jiao | Zendy; Shengmao Fu | Zendy

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Global Behavior for a Strongly Coupled Predator-Prey Model with One Resource and Two Consumers

Author(s) -

Yujuan Jiao,

Shengmao Fu

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/183285

Subject(s) - mathematics , functional response , lyapunov function , predation , resource (disambiguation) , exponential stability , stability (learning theory) , predator , function (biology) , mathematical economics , mathematical optimization , control theory (sociology) , ecology , computer science , nonlinear system , artificial intelligence , biology , computer network , physics , control (management) , quantum mechanics , machine learning , evolutionary biology

We consider a strongly coupled predator-prey model with one resource and two consumers, in which the first consumer species feeds on the resource according to the Holling II functional response, while the second consumer species feeds on the resource following the Beddington-DeAngelis functional response, and they compete for the common resource. Using the energy estimates and Gagliardo-Nirenberg-type inequalities, the existence and uniform boundedness of global solutions for the model are proved. Meanwhile, the sufficient conditions for global asymptotic stability of the positive equilibrium for this model are given by constructing a Lyapunov function. © 2012 Yujuan Jiao and Shengmao Fu.

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