## University of Sydney Algebra Seminar

# Yi Ming Zou (University of Wisconsin at Milwaukee)

## Wednesday 20 March, 12-1pm, Place: Carslaw 375

## Linear Dynamical Systems over Finite Commutative Rings

Polynomial dynamical systems over finite fields or rings provide a useful tool for studying network dynamics, such as those of gene regulatory networks. In this talk, I will discuss linear dynamical systems over finite commutative rings. The limit cycles of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. The extension to the general finite commutative rings is natural and has applications. To address the difficulties in the general ring setting, we developed a computational approach. In an earlier work, we gave an efficient algorithm to determine whether a linear dynamical system over a finite commutative ring is a fixed-point system or not. In a more recent work, we further analyzed the structure of these systems and described a method to determine the limit cycles.