Algebra Seminar: Yi Ming -- Linear Dynamical Systems over Finite Commutative Rings

Yi Ming Zou (University of Wisconsin at Milwaukee) 

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

Title: Linear Dynamical Systems over Finite Commutative Rings 

Abstract: 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.