Nonlinear Random Dynamical Systems on Networks: a Tutorial of Basic Theory
Dr. Jorge Ramirez
, Oak Ridge National Laboratory
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.