Faculty of Engineering and Natural Sciences
Stability of delay differential equations near Hopf bifurcation
Fatihcan M. Atay
Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
Time delays occur naturally in all physical and biological systems. They are, however, usually neglected in models due to increased mathematical difficulties. Indeed, the stability of equilibria of delay differential equations is a challenging mathematical problem, and precise analytical results are few except in certain special cases. In this talk I will present a framework that allows the stability analysis of systems of functional differential equations that are near a generic Hopf bifurcation. Following this, I will give solutions to two recent problems of interest in the area of dynamical systems. The first one is to characterize the effect of network topology on the stability of interconnected systems with time delays. The second one is to understand the relationship between discrete and distributed feedback delays, resolving some conjectures in the existing literature.
Dr. Fatihcan Atay has received a B.S. degree from Mechanical Engineering and an M.S. from Systems and Control Engineering department, both in Boğaziçi University. He then received an Sc.M and a Ph.D from Applied Mathematics at Brown University in 1991 and 1994 respectively. He has been an Assistant Professor at Koc University for 4 years and has worked at Artesis-Arcelik as a senior research scientist.
Since 2002, he has been working at Max Planck Institute for Mathematics in the Sciences as a visiting scientist.
His research interests are Nonlinear dynamical systems, delay differential equations, control theory, delayed feedback systems, coupled oscillators and maps, complex networks, mathematical biology, industrial mathematics.
December 27, 2007, 14:40, FENS 2019