Dynamics and Optimal Taxation Control in a Bioeconomic Model with Stage Structure and Gestation Delay
Joint Authors
Zhang, Yi
Bai, Fenglan
Zhang, Qing-ling
Source
Mathematical Problems in Engineering
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-07-10
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
A prey-predator model with gestation delay, stage structure for predator, and selective harvesting effort on mature predator is proposed, where taxation is considered as a control instrument to protect the population resource in prey-predator biosystem from overexploitation.
It shows that interior equilibrium is locally asymptotically stable when the gestation delay is zero, and there is no periodic orbit within the interior of the first quadrant of state space around the interior equilibrium.
An optimal harvesting policy can be obtained by virtue of Pontryagin's Maximum Principle without considering gestation delay; on the other hand, the interior equilibrium of model system loses as gestation delay increases through critical certain threshold, a phenomenon of Hopf bifurcation occurs, and a stable limit cycle corresponding to the periodic solution of model system is also observed.
Finally, numerical simulations are carried out to show consistency with theoretical analysis.
American Psychological Association (APA)
Zhang, Yi& Zhang, Qing-ling& Bai, Fenglan. 2012. Dynamics and Optimal Taxation Control in a Bioeconomic Model with Stage Structure and Gestation Delay. Mathematical Problems in Engineering،Vol. 2012, no. 2012, pp.1-17.
https://search.emarefa.net/detail/BIM-1029770
Modern Language Association (MLA)
Zhang, Yi…[et al.]. Dynamics and Optimal Taxation Control in a Bioeconomic Model with Stage Structure and Gestation Delay. Mathematical Problems in Engineering No. 2012 (2012), pp.1-17.
https://search.emarefa.net/detail/BIM-1029770
American Medical Association (AMA)
Zhang, Yi& Zhang, Qing-ling& Bai, Fenglan. Dynamics and Optimal Taxation Control in a Bioeconomic Model with Stage Structure and Gestation Delay. Mathematical Problems in Engineering. 2012. Vol. 2012, no. 2012, pp.1-17.
https://search.emarefa.net/detail/BIM-1029770
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1029770