Coexistence and optimal control problems for a degenerate predator-prey model

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:378

Article

Allegretto, W.²  Fragnelli, G.³  Nistri, P.¹  Papini, D.¹ 

[1] Univ Siena, Dipartimento Ingn Informaz, I-53100 Siena, Italy

[2] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

[3] Univ Bari, Dipartimento Matemat, I-70125 Bari, Italy

关键词: Degenerate parabolic equations;    Positive periodic solutions;    Optimal control problems;   

DOI  :  10.1016/j.jmaa.2010.12.036

来源: Elsevier

【 摘 要 】

In this paper we present a predator-prey mathematical model for two biological populations which dislike crowding. The model consists of a system of two degenerate parabolic equations with nonlocal terms and drifts. We provide conditions on the system ensuring the periodic coexistence, namely the existence of two non-trivial non-negative periodic solutions representing the densities of the two populations. We assume that the predator species is harvested if its density exceeds a given threshold. A minimization problem for a cost functional associated with this process and with some other significant parameters of the model is also considered. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free