Controllability and stabilization of a nonlinear hierarchical age-structured competing system

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.

Keywords

• hierarchy of age
• population system
• competition
• controllability
• fan-glicksberg fixed points