Life is nonlinear: Living the life in this particular universe is interesting because almost every natural phenomenon is nonlinear. It, thus, is inevitable that an inquisitive and self-aware mind would undertake the curiously adventurous journey of trying to understand the order and chaos in nonlinear systems. But sadly(?!), life is short and there are only twenty-four hours in each Earth-day. A mortal being cannot even dream of understanding each and every nonlinear phenomenon in the known and the unknown parts of the cosmos. Consequently, one has to compromise and patiently nibble into the gigantic and highly branched research area(s) of nonlinear dynamics. I try doing exactly that.

My current research interests are in the following nonlinear dynamical systems:
  1. Games: Exciting interdisciplinary topics of research in complex systems, such as evolutionary game dynamics, are very much in vogue. The concept of evolution is easily among the most revolutionary leaps in human understanding of nature. Evolutionary game dynamics lies right in the overlapping area of the nonlinear dynamics, the stochastic processes and statistical mechanics, the game theory, and the theory of evolution. For the last two years, I have been trying to understand the process of evolution through nonlinear dynamical systems. Some of my primary interests are: (i) understanding how dynamical solutions correspond to the game theoretic equilibria, (ii) evolution of cooperation in evolutionary games, and (iii) connection between population games in finite and infinite populations.
  2. Chaos: I am interested in gaining insights into the nature and the significance of chaos in autonomous nonintegrable Hamiltonian systems with very few degrees of freedom, e.g., swinging spring pendulum; and subsequently, my goal is to understand the meaning and implications of quantization of such systems. Besides, I am also interested in studying how and when coupled chaotic oscillators can be made to synchronize. Of late, I have started to flirt with quantum chaos, i.e., the quantum mechanics of classically chaotic systems.
  3. Turbulence: Specifically, using lower dimensional models, e.g., the shell models, of turbulence, I want to understand why rotation makes many statistical features of the homogeneous isotropic three-dimensional turbulence mimic that of the two-dimensional turbulence.