My areas of research include (a) Nonlinear Time Series Analysis using the measures of Complex Networks, (b) To study the effect of additive noises (white and colored noise) on topology of chaotic systems. These areas of research are applicable to different fields of science, especially in astrophysics, to analyze the light curve from variable stars and black hole systems which give us the information regarding the underlying nonlinear processes leading to the emission of light curves. This research can also be applied in the field of medical sciences for analyzing the E.C.G (Electrocardiography) and E.E.G (Electroencephalography) data. The E.C.G data contains the information regarding the dynamics of the heart and the E.E.G data hold the information about the complex processes that take place inside the brain. So the study on the E.C.G data helps one to predict the chances of occurring the different cardiac problems and that of E.E.G data helps to understand more on the underlying dynamics which assist to predict the occurrence of epileptic conditions in a patient. The collaborators of my reserach are (1.) Dr. K. P. Harikrishnan (my research guide), Associate Professor, The Cochin College (2.) Dr. Ranjeev Misra, Professor, IUCAA, Pune (3.) Dr. G Ambika, Professor and Dean of Academics, IISER, Pune. In the following section, I would like to give some basic idea about my research field, its importance and the works we have completed.
From my knowledge, the dynamical systems are usually modelled by a set of coupled differential equations or difference equations, called “maps”. And in the case of real world systems, the information regarding the temporal evolution (evolution in time) is commonly available in the form of a scalar time series of a single variable (Uni-variate time series). The goal of the time series analysis is to understand the dynamics occurring behind some observed time – ordered data. The time series of any dynamical process is the realisation of its dynamics in time. Let me give some examples of the real world time series data:
- The light curve from a star is the time series data that gives information about the underlying dynamics taking place inside a star (see image)
- The data from an Electrocardiography (E.C.G) gives the information about the dynamics of the electrical activity happening inside heart (see image)
- An Electroencephalography (E.E.G) tracks and records brain wave patterns which deliver data about the electrical activity occurring inside the brain.