SEMINAR

Computation of Invariant Measures

School of Mathematical Sciences
University of Southern Mississippi

ABSTRACT

In various fields of physical sciences, such as neural networks, condensed matter physics, and reaction-diffusion system, many problems are reduced to the existence and computation of the density of an absolutely continuous invariant probability measure of a non-singular transformation, which can be obtained by computing the fixed density of the so-called Frobenius-Perron operator which can be view as a differential-integral operator.

In this talk we first use Ulam's method to study two numerical algorithms for the computation of fixed densities of Frobenius-Perrron operators: iteration algorithm and Gaussian algorithm. Then we discuss two methods to implement the companion matrix in Ulam's method: Monte Carlo (MC) method and modified Monte Carlo (MMC) method. MC/MMC allow us to find a good approximation even though the analytic expression of the system is too complicated to find the inverse image of a set under the transformation of the system. Computational results for various models of dynamical systems are presented and investigated.

WHERE: TEC 251

WHEN(day): Friday, November 20th, 1998

WHEN(time): 2:00pm

EVERYBODY IS INVITED