Abstract
We study optimal birth policies for three age-dependent populations in a predator-prey system, which is controlled by fertility. New results on problems with free final time and integral phase constraints are presented, the approximate controllability of system is discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Burton, T.A.: Modelling and Differential Equations in Biology. Dekker, New York (1980)
Chan, W.L., Guo, B.Z.: Optimal birth control of population dynamics. J. Math. Anal. Appl. 144, 532–552 (1989)
Chan, W.L., Guo, B.Z.: Optimal birth control of population dynamics. Part 2. Problems with free final time, phase constraints, and mini-max costs. J. Math. Anal. Appl. 146, 523–539 (1990)
Chan, W.L., Guo, B.Z.: Overtaking optimal control problems of age-dependent populations with infinite horizon. J. Math. Anal. Appl. 150, 41–53 (1990)
Anita, S.: Optimal harvesting for a nonlinear age-dependent population dynamics. J. Math. Anal. Appl. 226, 6–22 (1998)
Anita, S., Iannelli, M., Kim, M.-Y., Park, E.-J.: Optimal harvesting for periodic age-dependent population dynamics. SIAM J. Appl. Math. 58, 1648–1666 (1998)
Albrecht, F., Gatzke, H., Haddad, A., Wax, N.: On the control of certain interacting populations. J. Math. Anal. Appl. 53, 578–603 (1976)
Lenhart, S., Liang, M., Protopopescu, V.: Optimal control of boundary habitat hostility for interacting species. Math. Mech. Appl. Sci. 22, 1061–1077 (1999)
Crespo, L.G., Sun, J.Q.: Optimal control of populations of competing species. Nonlinear Dyn. 27, 197–210 (2002)
Fistera, K.R., Lenhart, S.: Optimal control of a competitive system with age-structure. J. Math. Anal. Appl. 291(2), 526–537 (2004)
He, Z.-R.: Optimal birth control of age-dependent competitive species. J. Math. Anal. Appl. 296, 286–301 (2004)
Luo, Z., He, Z.-R., Li, W.-T.: Optimal birth control for an age-dependent n-dimensional food chain model. J. Math. Anal. Appl. 287, 557–576 (2003)
Yu, J.Y., Guo, B.Z., Zhu, G.T.: Control Theory of Population Distributional Parameter Systems. Press of Central China University of Science and Technology, Wuhan (1999) (in Chinese)
Girsanov, I.V.: Lectures on Mathematical Theory of Extremum Problem. Lecture Notes in Eco. Math. Sys., vol. 67. Springer, New York (1972)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work is supported by the National Natural Science Foundation of the People’s Republic of China (10771048) and ‘Qing Lan’ Talent Engineering Funds (QL-05-18A) by Lanzhou Jiaotong University.
Rights and permissions
About this article
Cite this article
Luo, Z., Xing, T. & Li, X. Optimal birth control of free horizon problems for predator-prey system with age-structure. J. Appl. Math. Comput. 34, 19–37 (2010). https://doi.org/10.1007/s12190-009-0302-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12190-009-0302-1