Title: Synchronization & Bifurcations in Brain Activity

Marat Akhmet

Middle East Technical University, Turkey


Dr. Marat Akhmet, (Ph.D.), now is a Professor at the Department of Mathematics, Middle East Technical University, Turkey. He got his B Sc in mathematics at Aktobe State University, Kazakhstan, M Sc and Ph.D. in Differential Equations and Mathematical Physics at Kiev State University, Ukraine. Currently Dr. Marat Akhmet’s researches focus on the dynamical models and differential equations. He has published five books and more than a hundred and thirty scientific papers. In the last several years, he has been investigating dynamics of neural networks: periodic and almost periodic motions, stability, synchronization, chaos and its control.


Complexity and synchronization in models are necessary for research in neuroscience.   In our talk the complexity will be present through special type of bifurcations - the medusas bifurcations in the Cowan-Wilson model, they have been introduced in our recent papers.   Synchronization of biological integrate-and-fire oscillators will be discussed considering the C. Peskin model.   The collective behavior of biological and chemical oscillators is a fascinating topic that has attracted a lot of attention in the last 50 years.  The integrate-and-fire model of the cardiac pacemaker was developed by C.Peskin to a  population of identical pulse-coupled oscillators.   The model has been widely adapted for neuroscience. In the present research we give a solution of the second conjecture of Peskin. The talk will consists of main results, simulations and discussion of  possible extensions. We will discuss what kind of benefits can be obtained from the study for the artificially intelligent systems, robotics and electronics.