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

• Main Authors: Ze-Rong He, Nan Zhou
• Format: Article
• Language: English
• Published: Texas State University 2020-06-01
• Series: Electronic Journal of Differential Equations
• Subjects: hierarchy of age; population system; competition; controllability; fan-glicksberg fixed points
• Online Access: http://ejde.math.txstate.edu/Volumes/2020/58/abstr.html

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.