Control of a predator-prey system with intraspecies competition

Kolmanovskii, V. B.; Королева, Н Ю

doi:10.1016/0021-8928(91)90105-4

Cited by 2 publications

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“…We will not assume that all the elements of b have the same sign, so that the same control action can benefit a species i (where b i > 0) and harm a species j (where b j < 0). Such a control objective was already pursued in (Goh et al, 1974;Kolmanovskii and Koroleva, 1991) through optimal control theory, but those were limited to two-dimensional systems; a preliminary study of accessibility for n-dimensional LotkaVolterra systems was however given in (DeLeenheer and Aeyels, 2000) while a first controller for those ndimensional systems was given in (Gouzé, 1994).…”

Section: Introductionmentioning

confidence: 99%

Positive Control of Lotka-Volterra Systems

Grognard

Gouzé

2005

IFAC Proceedings Volumes

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Section: Introductionmentioning

confidence: 99%

Positive Control of Lotka-Volterra Systems

Grognard

Gouzé

2005

IFAC Proceedings Volumes

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Irreversible prey diapause as an optimal strategy of a physiologically extended Lotka–Volterra model

2012

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We propose an optimal control framework to describe intra-seasonal predator-prey interactions, which are characterized by a continuous-time dynamical model comprising predator and prey density, as well as the energy budget of the prey over the length of a season. The model includes a time-dependent decision variable for the prey, representing the portion of the prey population in time that is active, as opposed to diapausing (a state of physiological rest). The predator follows autonomous dynamics and accordingly it remains active during the season. The proposed model is a generalization of the classical Lotka-Volterra predator-prey model towards non-autonomous dynamics that furthermore includes the effect of an energy variable. The model has been inspired by a specific biological system of predatory mites (Acari: Phytoseiidae) and prey mites (so-called fruit-tree red spider mites) (Acari: Tetranychidae) that feed on leaves of apple trees--its parameters have been instantiated based on laboratory and field studies. The goal of the work is to understand the decisions of the prey mites to enter diapause (a state of physiological rest) given the dynamics of the predatory mites: this is achieved by solving an optimization problem hinging on the maximization of the prey population contribution to the next season. The main features of the optimal strategy for the prey are shown to be that (1) once in diapause, the prey does not become active again within the same season and hence diapause is an irreversible process; (2) for the vast majority of parameter space, the portion of prey individuals entering diapause within the season does not decrease in time; (3) with an increased number of predators, the optimal population strategy for the prey is to start diapause earlier and to enter diapause more gradually. This optimal population strategy will be studied for its ESS properties in a sequel to the work presented in this article.

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Control of a predator-prey system with intraspecies competition

Cited by 2 publications

References 0 publications

Positive Control of Lotka-Volterra Systems

Positive Control of Lotka-Volterra Systems

Irreversible prey diapause as an optimal strategy of a physiologically extended Lotka–Volterra model

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