The Library
Optimal impulsive harvesting on non-autonomous Beverton-Holt difference equations
Tools
Tang, Sanyi, Cheke, Robert A. and Xiao, Yanni (2006) Optimal impulsive harvesting on non-autonomous Beverton-Holt difference equations. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 65 (12). pp. 2311-2341. doi:10.1016/j.na.2006.02.049 ISSN 0362-546X.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://dx.doi.org/10.1016/j.na.2006.02.049
Abstract
Many recent advances in the theory of the optimal economic exploitation of renewable fish resources have been gained by applying optimal control theory. However, despite these successes, much less is known about how seasonal environments affect the maximum sustainable yield (MSY) (or population persistence) and any effects of relations between intensity and frequency of harvesting. Assuming that fish populations follow Beverton-Holt equations we investigated impulsive harvesting in seasonal environments, focusing on both economic aspects and resource sustainability. We first investigated the existence and stability of a periodic solution and its analytic formula, and then showed that the population persistence depends on the intensity and frequency of harvesting. With the MSY as a management objective, we investigated optimal impulsive harvesting policies. The optimal harvesting effort that maximizes the sustainable yield, the corresponding optimal population level, and the MSY are obtained by using discrete Euler-Lagrange equations and product formulae, and their explicit expressions were obtained in terms of the intrinsic growth rate, the carrying capacity, and the impulsive moments. These results imply that harvest timing is of crucial importance to the MSY Since impulsive differential equations incorporate elements of continuous and discrete systems, we can apply all results obtained for Beverton-Holt equations with impulsive effects to periodic logistic equations with impulsive harvesting. (c) 2006 Elsevier Ltd. All rights reserved.
Item Type: | Journal Article | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | ||||
Publisher: | PERGAMON-ELSEVIER SCIENCE LTD | ||||
ISSN: | 0362-546X | ||||
Official Date: | 15 December 2006 | ||||
Dates: |
|
||||
Volume: | 65 | ||||
Number: | 12 | ||||
Number of Pages: | 31 | ||||
Page Range: | pp. 2311-2341 | ||||
DOI: | 10.1016/j.na.2006.02.049 | ||||
Publication Status: | Published |
Data sourced from Thomson Reuters' Web of Knowledge
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |