Mechanical and Aerospace Engineering
Department Seminar Series
8/14 (Friday) 3:00 pm – 4:00 pm RH200
Dynamics of randomly switched dynamical networks: windows of opportunity
Igor Belykh, Ph.D.
Department of Mathematics and Statistics
Georgia State University
We study dynamical networks whose topology and intrinsic parameters stochastically change, on a time scale that ranges from fast to slow. If the stochastic switching is fast enough, we expect the switching system to follow the averaged system where the dynamical law is given by the expectation of the stochastic variables. We ask the question under what conditions a solution of the randomly switched system converges to an attractor of the averaged system. The answer contains various subtleties and depends on whether or not the attractor in the averaged system is unique and whether it is an invariant set for all switching sequences. Beyond fast switching, we reveal unexpected windows of intermediate switching frequencies in which a dynamical regime (synchronization, for example) becomes stable despite the instability of the averaged/fast-switching network.
Igor Belykh received his Ph.D. degree in applied mathematics in 2000 from the Andronov Chair at the Lobachevsky State University of Nizhny Novgorod, Russia. He held a post-doctoral position at the Laboratory of Nonlinear Systems at Swiss Federal Institute of Technology in Lausanne from 2001 to 2005. Currently, he is a tenured Associate Professor of Applied Mathematics with a joint appointment at the Neuroscience Institute at Georgia State University, Atlanta, GA, USA. He is also an Associate Member of the Center for Nonlinear Science at Georgia Institute of Technology. His research interests lie in dynamical Systems and their applications in biology, neuroscience, and engineering. Dr. Belykh is on the Editorial Board of six international journals, including the SIAM Journal on Applied Dynamical Systems, the International Journal of Bifurcation and Chaos, and the IEEE Transactions on Circuits and Systems I, where he received the Best Associate Editor Award for the 2012–2013 term.