HYBRID EVENT: You can participate in person at Baltimore, Maryland, USA or Virtually from your home or work.

10th Edition of International Conference on Neurology and Brain Disorders

October 21-23, 2024

October 21 -23, 2024 | Baltimore, Maryland, USA
INBC 2018

Marat Akhmet

Speaker at  - Marat Akhmet
Middle East Technical University, Turkey
Title : Synchronization and chaos in brain activity


We will consider two subjects of nonlinear dynamics: synchronization of integrate-and-fire biological oscillators; global chaos in neural networks and discuss their importance for brain activity from the dynamical systems and information dynamics point of view. 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 processes were developed by   C. Peskin to a population of identical pulse-coupled oscillators. It was conjectured that the model self-synchronizes such that:  for arbitrary initial conditions, the system approaches a state in which all the oscillators are firing synchronously; b) this remains true even when the oscillators are not quite identical. The first conjecture is solved by C. Peskin for a system with two oscillators, and R. Mirollo and S. Strogatz for the generalized model of two and more oscillators (J. Phys. A 21: L699–L705, 1988). The second conjecture was solved in the paper by M. Akhmet (Nonlinear Stud. 18:313–327, 2011). There are still many issues related to the nature and types of couplings. The couplings may be impulsive, continuous, delayed, or advanced, and oscillators may be locally or globally connected. Consequently, it is reasonable to consider various ways of synchronization if one wants the biological and mathematical analyses to interact productively. We investigate the integrate-and-?re model in both cases— one with identical and another with not-quite-identical oscillators. A combination of continuous and pulse couplings that sustain the ?ring in unison is carefully constructed. Moreover, we obtain conditions on the parameters of continuous couplings that make possible a rigorous mathematical investigation of the problem. In the present talk   we will discuss the role of synchronization and desynchronization for the brain activity.


Dr. Marat Akhmet is currently a Professor at Department of Mathematics, Middle East Technical University, Ankara, Turkey. He got his B.S. degree in mathematics at Aktobe State University, Kazakhstan, and Ph.D. degree 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 six books and more than a hundred and fifty scientific papers. In the last several years, he has been investigating dynamics of neural networks, periodic and almost periodic motions, stability, chaos and fractals.