Research

After M. Sc. Degree I underwent a Summer Research Program, supported by Indian Academy of Sciences (IASc), Bangalore, working under the Supervision of Prof. M. Lakshmanan at Centre for Nonlinear Dynamics (which is recognized as one of the top-ranking Centres of excellence in nonlinear dynamics at the national and international levels), Bharathidasan University, Tiruchirappalli from May – June 2007. During this period I have mastered all the techniques associated with nonlinear dynamics and made deep inroads into the study of bifurcation, chaos and synchronization of nonlinear dynamical systems. I have also learned to solve the nonlinear differential equations numerically using FORTRAN – 77 and C programs during this research program.

After that I have joined as a full-time doctoral student with Prof. M. Lakshmanan at Centre for Nonlinear Dynamics, Bharathidasan University, Tiruchirappalli and immediately start to work with my Ph. D. problems in time-delay systems. In particular, significant contributions have been made to understand the dynamical states, their stability, bifurcation, chaotic/hyperchaotic behavior and synchronization transition in nonlinear time-delay systems.

Nonlinear time-delay dynamical systems are essentially infinite dimensional in nature and are difficult to handle both analytically and numerically. Sustained efforts have been made to study these systems and I have brought out several fascinating features in these systems with regular network configuration. Specifically, existence of global phase synchronization via clustering of oscillators with nearest frequencies, partial phase synchronization, global intermittent synchronization, sequential and immediate transition to complete synchronization, global generalized synchronization, zero-lag synchronization, inverse phase synchronization, inverse synchronization, delay induced/enhanced coherent chaotic oscillations, etc., have been identified in regular networks of time-delay systems. The results are published in prestigious International scientific journals.

In addition, the numerical investigations on synchronization transition are also corroborated with asymptotic stability condition using Krasovskii-Lyapunov functional theory in most cases. Further, most of the above synchronizations are also confirmed experimentally using time-delay electronic circuits. Specifically, the framework of localized sets, which is a more general and efficient concept that can even work for highly non-phase-coherent hyperchaotic attractors when all the other conventional methods fail to characterize phase synchronization, is implemented experimentally.

During my doctoral studies, I have also made investigation on experimental realization of strange non-chaotic attractors (SNAs) using a nonlinear series LCR circuits with nonsinusoidal force.

I have also worked on several research projects funded by different funding agencies in India, which enable me to gain some experience on administrative aspects of such projects.

At the moment I am working as a Research Scientist and pursuing my research on emergent collective behavior in complex networks of nonlinear dynamical systems with time-delay.