Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 58, pp. 1-16.

Title: Controllability and stabilization of a nonlinear hierarchical 
       age-structured competing system
       
Authors: Ze-Rong He (Hangzhou Dianzi Univ., Hangzhou, China)
         Nan Zhou.  (Hangzhou Dianzi Univ., Hangzhou, China)

Abstract:
 This article concerns the approximate controllability of a biological system,
 which is composed of two hierarchical age-structured competing species.
 Basing on a controllability result of linear system, we prove that the nonlinear
 system is approximately controllable by means of a fixed point theorem for
 multi-valued mappings. To fix a suitable control policy, we deal with an
 optimal control problem and established the existence of the unique optimal strategy.
 In addition, the stabilization problem of the system is also considered.
 
Submitted November 19, 2019. Published June 11, 2020.
Math Subject Classifications: 92D05, 47D06, 35B35.
Key Words: Hierarchy of age; population system; competition; controllability;
           Fan-Glicksberg fixed points.