Brief research statement and achievements
I. Amplitude death and Oscillation death Oscillation quenching is an emergent and intriguing phenomenon that has been the topic of extensive research in diverse fields such as physics, biology, and engineering. There are two distinct types of oscillation quenching processes: amplitude death (AD) and oscillation death (OD). Although, AD and OD are two structurally different phenomena (their genesis and manifestations are different) but for many years they are (erroneously) treated in the same footing. Only recently, the much-needed distinctions between AD and OD has been established. In this field we have contributed some pioneering researches: examples include
II. Nonlinear Dynamics in the Quantum regime: Exploring nonlinear dynamics in the open quantum systems has gained much attention in recent years. The well known concepts of nonlinear dynamics such as oscillation of a single unit, and emergent behaviors of coupled oscillatory units, such as synchronization, have recently been explored in the quantum regime. The extension of the techniques used in the so-called classical nonlinear dynamics to the quantum regime is not always straightforward. Understanding of nonlinear behavior in the quantum domain is based on the formalism of open quantum system that requires the solution of quantum master equations. Also, phase space representation of quantum system which involves quasi probability function (e.g. Wigner function) plays a crucial role in this endeavor. We are at present exploring symmetry-breaking phenomena in quantum oscillators.
III. Symmetry breaking in a network of coupled oscillators: Chimera State The chimera state is an intriguing and counterintuitive spatiotemporal state that has been in the center of active research over the past decade. In this state the population of coupled identical oscillators spontaneously splits into two incongruous domains: In one domain the neighboring oscillators are synchronized, whereas in another domain the oscillators are desynchronized. The strong current interest in chimeras may be attributed to their possible connection with several phenomena in nature, like unihemispheric sleep of dolphins and certain migratory birds, ventricular fibrillation, and power grid networks. Recently, chimera patterns have been found in models from ecology, SQUID metamaterials, and quantum systems showing their omnipresence in the macroscopic as well as in the microscopic world. Our group has made some pioneering contributions towards the understanding of this state:
III. Mathematical Biology
IV. Chaotic & hyperchaotic time-delayed dynamical systems: Design and Synhronization We invented many delayed dynamical systems that show chaotic and hyperchaotic behavior. Those systems are implemented with off-the-shelf electronic circuits that can be controlled and synchronized for the application purposes. Studies on different synchronization phenomena of time-delayed hyperchaotic systems. Our group reported the first experimental and theoretical observation of synchronization in chaotic and hyperchaotic time-delay systems coupled by environmental coupling. [Nonlinear Dynamics Vol. 73, pp. 2025-2048. 2013, Nonlinear Dyn., Vol. 70 (1), pp. 721-734 ( 2012), Int. J. Bifurcation and Chaos, 23, 1330020 (2013), Nonlinear Dyn. Vol. 83, pp 2331-2347, 2015] V. Chaotic electronic circuits and phase-locked loops We invented some new chaotic electronic circuits, study their synchronization behavior and explore their potential for application in chaos based electronic communications. Also, we extensively studied on Digital phase locked loop (DPLL), which is one of the basic building blocks of modern communication systems. We explore the nonlinear dynamics of DPLL in the whole parameter space and quantify its chaotic dynamics. Also, based upon the insight of the nonlinear behaviour, we propose many modifications to the structure of DPLL for obtaining better system response in its application potentiality [Nonlinear Dynamics, Vol.68(4), 565-573 (2012); Vol. 62(4), 859–866 (2010); Int. J. Electron. Commun. (AEU) 66 (2012) 593– 597 ; CHAOS, Vol. 24, No.1, 013116, 2013, IJBC, 26 (5), 1650076, 2016, [Int. J. Bifurcation and Chaos, Vol. 22 (12), 1230044; Vol. 23, No. 8, 2013, pp 1330029, etc.] |