The next meeting of the

Interdisciplinary Seminar on Biomathematics and Scientific Computing

will be held on July 4, 2019  (Thursday), at 3.00 p.m. in Room 403 of IMI-BAS.

A talk on:

Ergodicity and loss of capacity for a family of concave random maps

will be delivered by Prof. Peter Hinow (University of Wisconsin-Milwakee, САЩ)

Abstract. Random fluctuations of an environment are common in ecological and economical settings. We consider a family of concave maps on the unit interval, f_λ(x)=x(1+λ-x), that model a self-limiting growth behavior. The maps are parametrized by an independent, identically distributed random variable λ with values in the unit interval. We show the existence of a unique invariant ergodic measure of the resulting random dynamical system for arbitrary parameter distributions supported on certain subintervals of [0,1]. Moreover, there is an attenuation of the mean of the state variable compared to the constant environment with the averaged parameter. We also provide an example of a family of just two maps such that the invariant probability measure is supported on a Cantor set. This is joint work with Ami Radunskaya (Pomona College, CA).