Existence and Uniqueness of Positive Periodic Solutions for a Delayed Predator-Prey Model with Dispersion and Impulses | Zendy

Zhenguo Luo | Zendy; Liping Luo | Zendy; Liu Yang | Zendy; Zhenghui Gao | Zendy; Yunhui Zeng | Zendy

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Existence and Uniqueness of Positive Periodic Solutions for a Delayed Predator-Prey Model with Dispersion and Impulses

Author(s) -

Zhenguo Luo,

Liping Luo,

Liu Yang,

Zhenghui Gao,

Yunhui Zeng

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/592543

Subject(s) - uniqueness , mathematics , verifiable secret sharing , predation , stability (learning theory) , coincidence , population , functional response , population model , lyapunov function , predator , epidemic model , set (abstract data type) , biological dispersal , mathematical analysis , nonlinear system , ecology , computer science , physics , alternative medicine , pathology , sociology , biology , quantum mechanics , machine learning , programming language , medicine , demography

An impulsive Lotka-Volterra type predator-prey model with prey dispersal in two-patch environments and time delays is investigated, where we assume the model of patches with a barrier only as far as the prey population is concerned, whereas the predator population has no barriers between patches. By applying the continuation theorem of coincidence degree theory and by means of a suitable Lyapunov functional, a set of easily verifiable sufficient conditions are obtained to guarantee the existence, uniqueness, and global stability of positive periodic solutions of the system. Some known results subject to the underlying systems without impulses are improved and generalized. As an application, we also give two examples to illustrate the feasibility of our main results

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