Stability and controllability of cycled dynamical systems

Abstract In this paper, we consider a new type of dynamical systems called cycled dynamical systems (CDSs) based on the cell growth and division process. Firstly, the existence and uniqueness of cycled solutions of CDSs are studied. Secondly, we present the solutions of the CDSs through an appropriate cycled Cauchy matrix. Moreover, the stability of the linear homogeneous problems, linear perturbation problems and nonlinear problems is analyzed. Next, we investigate the controllability of linear and nonlinear CDSs. Finally, theoretical results are illustrated by providing examples.