Author:
Liu Rong,Zhou Nan,He Ze-Rong
Abstract
AbstractThis paper discusses the optimal control problems for a nonlinear age-structured two-species model, where elder individuals are more competitive than younger ones, and each species is described by a nonlinear integropartial differential equation with a global feedback boundary condition. First, we establish the existence of a unique nonnegative bounded solution by means of frozen coefficients and the fixed-point theorem. More importantly, we discuss the least deviation-cost problem and the most benefit-cost problem. For the least deviation-cost problem, the existence of an optimal strategy is established by means of Ekeland’s variational principle, and the minimum principle is obtained via an adjoint system. Meanwhile, the corresponding results for the most benefit-cost problem are given. In addition, some numerical experiment results are presented to examine the effects of parameters on the optimal policies and indexes.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Shanxi Province
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference41 articles.
1. Magal, P., Ruan, S., et al.: Structured-Population Models in Biology and Epidemiology. Springer, Berlin (2008)
2. Aniţa, S.: Analysis and Control of Age-Dependent Population Dynamics. Kluwer Academic, Dordrecht (2000)
3. Iannelli, M.: Mathematical Theory of Age-Structured Population Dynamics. Giardini Editori, Pisa (1995)
4. Aniţa, L., Aniţa, S.: Note on some periodic optimal harvesting problems for age-structured population dynamics. Appl. Math. Comput. 276, 21–30 (2016)
5. Li, L., Ferreira, C., Ainseba, B.: Optimal control of an age-structured problem modelling mosquito plasticity. Nonlinear Anal., Real World Appl. 45, 157–169 (2019)