On an optimal control problem related to A.D. Bazykin’s general predator-prey model

We consider a controlled analog of A.D. Bazykin’s predator-prey model and study the time optimization problem for this model. Under broad assumptions, we prove the bangbang property of the optimal control for the optimization problem in question and obtain an upper bound for the number of points of...

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Bibliographic Details
Published in:	Differential equations Vol. 47; no. 11; pp. 1660 - 1667
Main Author:	Nikol’skii, M. S.
Format:	Journal Article
Language:	English
Published:	Dordrecht SP MAIK Nauka/Interperiodica 01-11-2011 Springer Nature B.V
Subjects:	Control Theory Difference and Functional Equations Differential equations Discontinuity Lotka-Volterra equations Mathematics Mathematics and Statistics Optimal control Optimization Ordinary Differential Equations Partial Differential Equations Population Predator-prey simulation Upper bounds Pontryagin Maximum Principle Optimal Control Problem Predator Population Prey Model Prey Population
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Summary:	We consider a controlled analog of A.D. Bazykin’s predator-prey model and study the time optimization problem for this model. Under broad assumptions, we prove the bangbang property of the optimal control for the optimization problem in question and obtain an upper bound for the number of points of discontinuity of the bang-bang optimal control. We also analyze the time optimization problem for the controlled analog of the Lotka-Volterra predatorprey model.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0012-2661 1608-3083
DOI:	10.1134/S0012266111110127