Nonlinear Random Dynamical Systems on Networks: a Tutorial of Basic Theory

Dr. Jorge Ramirez

Abstract: In this tutorial, we will look at some basic theory of random dynamical systems, defined by non-linear stochastic differential equations with an underlying graph structure. The concrete application I have in mind is large predator-prey networks in ecological dynamics, but the subject matter is very general. We will see how the classical Lyapunov theory can be extended to show existence, boundedness, stability, and the existence of stationary distributions for these problems. I will show some interesting results on the effects of adding noise to the structural properties of nonlinear dynamical systems. We will also show, through a simple but important example, how the underlying graph structure plays an important role in the effect of noise over the long term behavior of the solutions. This is joint work with Carlos Osorio at Universidad Nacional de Columbia-Unalmed.

Speaker’s Bio: Jorge is an applied mathematician, educator, and researcher. He was born and raised in Medellín, Colombia, where he attended engineering school. Later, he obtained a PhD degree in Mathematics at Oregon State University and held a postdoctoral position at the mathematics department of The University of Arizona. From 2009 until 2021, Jorge worked as an associate professor in mathematics in his hometown at Universidad Nacional de Colombia. He joined the Systems and Decision Sciences group at the Oak Ridge National Laboratory in February 2022 to conduct interdisciplinary research in the theory, modeling, and computation of stochastic processes applied to the natural and life sciences.

Last Updated: April 27, 2022 - 7:53 am