Research

My research interests are in the applications of dynamical systems and differential equations in biology and neuroscience. In particular, I want  to apply rigorous mathematical techniques, numerical and computational methods to model and analyze the way biological systems go in and out of sync.. The emergence of synchronous behaviors of coupled systems is the result of important mathematical and physical theories developed over the last few years. Regardless of these developments, scientists know less about the human brain than the universe. The emergence of a synchronous behavior of  a dynamical complex network is an interplay between the intrinsic dynamics of the system, the network topology and the coupling dynamics of the network. Motivated by neuronal networks, my research goal is to develop a mathematical framework for understanding synchronization in networks that are not linearly coupled.