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

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 ex...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2011-06, Vol.378 (2), p.528-540
Main Authors: Allegretto, W., Fragnelli, G., Nistri, P., Papini, D.
Format: Article
Language:English
Subjects:
Calculus of variations and optimal control
Degenerate parabolic equations
Exact sciences and technology
Mathematical analysis
Mathematics
Nonlinear algebraic and transcendental equations
Numerical analysis
Numerical analysis. Scientific computation
Optimal control problems
Partial differential equations
Positive periodic solutions
Sciences and techniques of general use
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Summary: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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2010.12.036