A bifurcation path to chaos in a time-delay fisheries predator-prey model with prey consumption by immature and mature predators

© 2016 International Association for Mathematics and Computers in Simulation (IMACS). Stage-structure models have been extensively applied in predator-prey systems. In this paper, we consider an application to fisheries. We assume that there is a single prey population and a predator population that...

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Main Authors: S. Boonrangsiman, K. Bunwong, Elvin J. Moore
Other Authors: South Carolina Commission on Higher Education
Format: Article
Published: 2018
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Online Access:https://repository.li.mahidol.ac.th/handle/123456789/43508
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spelling th-mahidol.435082019-03-14T15:04:34Z A bifurcation path to chaos in a time-delay fisheries predator-prey model with prey consumption by immature and mature predators S. Boonrangsiman K. Bunwong Elvin J. Moore South Carolina Commission on Higher Education Mahidol University King Mongkut's University of Technology North Bangkok Computer Science Mathematics © 2016 International Association for Mathematics and Computers in Simulation (IMACS). Stage-structure models have been extensively applied in predator-prey systems. In this paper, we consider an application to fisheries. We assume that there is a single prey population and a predator population that can be separated by reproduction ability into an immature and a mature stage, with a time delay for the immature to mature transition. Our model includes the new assumption that both predators are able to hunt the same prey, although at different rates. It is proved that the system has three nonnegative equilibrium points, namely, a trivial point with all populations zero, a predator-free equilibrium point, and a coexistence equilibrium point with all three populations non-zero. It is proved that the trivial equilibrium point is always unstable, that the predator-free equilibrium point is stable if and only if the coexistence equilibrium point does not exist, and that the coexistence point can either be stable for all time delays or become unstable if a Hopf bifurcation exists at a critical time delay. Numerical simulations show that the behavior of the system can become extremely complicated as the time delay is increased, with the long-time behavior changing from a stable coexistence equilibrium, to a limit cycle with one local maximum and minimum per cycle (Hopf bifurcation), to limit cycles with an increasing number of local maxima and minima per cycle, and finally to chaotic-type solutions. 2018-12-11T02:39:00Z 2019-03-14T08:04:34Z 2018-12-11T02:39:00Z 2019-03-14T08:04:34Z 2016-06-01 Article Mathematics and Computers in Simulation. Vol.124, (2016), 16-29 10.1016/j.matcom.2015.12.009 03784754 2-s2.0-84969326963 https://repository.li.mahidol.ac.th/handle/123456789/43508 Mahidol University SCOPUS https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84969326963&origin=inward
institution Mahidol University
building Mahidol University Library
continent Asia
country Thailand
Thailand
content_provider Mahidol University Library
collection Mahidol University Institutional Repository
topic Computer Science
Mathematics
spellingShingle Computer Science
Mathematics
S. Boonrangsiman
K. Bunwong
Elvin J. Moore
A bifurcation path to chaos in a time-delay fisheries predator-prey model with prey consumption by immature and mature predators
description © 2016 International Association for Mathematics and Computers in Simulation (IMACS). Stage-structure models have been extensively applied in predator-prey systems. In this paper, we consider an application to fisheries. We assume that there is a single prey population and a predator population that can be separated by reproduction ability into an immature and a mature stage, with a time delay for the immature to mature transition. Our model includes the new assumption that both predators are able to hunt the same prey, although at different rates. It is proved that the system has three nonnegative equilibrium points, namely, a trivial point with all populations zero, a predator-free equilibrium point, and a coexistence equilibrium point with all three populations non-zero. It is proved that the trivial equilibrium point is always unstable, that the predator-free equilibrium point is stable if and only if the coexistence equilibrium point does not exist, and that the coexistence point can either be stable for all time delays or become unstable if a Hopf bifurcation exists at a critical time delay. Numerical simulations show that the behavior of the system can become extremely complicated as the time delay is increased, with the long-time behavior changing from a stable coexistence equilibrium, to a limit cycle with one local maximum and minimum per cycle (Hopf bifurcation), to limit cycles with an increasing number of local maxima and minima per cycle, and finally to chaotic-type solutions.
author2 South Carolina Commission on Higher Education
author_facet South Carolina Commission on Higher Education
S. Boonrangsiman
K. Bunwong
Elvin J. Moore
format Article
author S. Boonrangsiman
K. Bunwong
Elvin J. Moore
author_sort S. Boonrangsiman
title A bifurcation path to chaos in a time-delay fisheries predator-prey model with prey consumption by immature and mature predators
title_short A bifurcation path to chaos in a time-delay fisheries predator-prey model with prey consumption by immature and mature predators
title_full A bifurcation path to chaos in a time-delay fisheries predator-prey model with prey consumption by immature and mature predators
title_fullStr A bifurcation path to chaos in a time-delay fisheries predator-prey model with prey consumption by immature and mature predators
title_full_unstemmed A bifurcation path to chaos in a time-delay fisheries predator-prey model with prey consumption by immature and mature predators
title_sort bifurcation path to chaos in a time-delay fisheries predator-prey model with prey consumption by immature and mature predators
publishDate 2018
url https://repository.li.mahidol.ac.th/handle/123456789/43508
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