Optimal control of swinging alliances in a parabolic competition model

E. Asano; S. Lenhart; V. Protopopescu

doi:10.1016/j.amc.2011.01.029

Optimal control of swinging alliances in a parabolic competition model

E. Asano, S. Lenhart, V. Protopopescu

Computational Sciences & Engineering Div

Research output: Contribution to journal › Article › peer-review

Abstract

A system of parabolic partial differential equations describes the interaction of three populations, modeling a dynamic competition/cooperation scenario. More precisely, two populations are always competing with each other, but the third population can switch the mode of alliance with the other two populations between cooperation and competition. The control is a function measuring the strength and nature of the alliance and the goal is to maximize the population with the swinging alliance while keeping the other two populations close to each other and minimizing the cost of the alliance action. Various scenarios are illustrated with numerical results.

Original language	English
Pages (from-to)	6838-6855
Number of pages	18
Journal	Applied Mathematics and Computation
Volume	217
Issue number	16
DOIs	https://doi.org/10.1016/j.amc.2011.01.029
State	Published - Apr 15 2011

Keywords

Competition
Cooperation
Opportunistic alliances
Optimal control
Parabolic PDEs

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10.1016/j.amc.2011.01.029

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abstract = "A system of parabolic partial differential equations describes the interaction of three populations, modeling a dynamic competition/cooperation scenario. More precisely, two populations are always competing with each other, but the third population can switch the mode of alliance with the other two populations between cooperation and competition. The control is a function measuring the strength and nature of the alliance and the goal is to maximize the population with the swinging alliance while keeping the other two populations close to each other and minimizing the cost of the alliance action. Various scenarios are illustrated with numerical results.",

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N2 - A system of parabolic partial differential equations describes the interaction of three populations, modeling a dynamic competition/cooperation scenario. More precisely, two populations are always competing with each other, but the third population can switch the mode of alliance with the other two populations between cooperation and competition. The control is a function measuring the strength and nature of the alliance and the goal is to maximize the population with the swinging alliance while keeping the other two populations close to each other and minimizing the cost of the alliance action. Various scenarios are illustrated with numerical results.

AB - A system of parabolic partial differential equations describes the interaction of three populations, modeling a dynamic competition/cooperation scenario. More precisely, two populations are always competing with each other, but the third population can switch the mode of alliance with the other two populations between cooperation and competition. The control is a function measuring the strength and nature of the alliance and the goal is to maximize the population with the swinging alliance while keeping the other two populations close to each other and minimizing the cost of the alliance action. Various scenarios are illustrated with numerical results.

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KW - Cooperation

KW - Opportunistic alliances

KW - Optimal control

KW - Parabolic PDEs

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SP - 6838

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JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 16

ER -

Optimal control of swinging alliances in a parabolic competition model

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