Neelima Gupte

Bio: Neelima Gupte is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: Intermittency & Coupled map lattice. The author has an hindex of 3, co-authored 11 publications receiving 34 citations. Previous affiliations of Neelima Gupte include Indian Institutes of Technology.

Spatial splay states and splay chimera states in coupled map lattices.

Abstract: We study the existence and stability of splay states in the coupled sine circle map lattice system using analytic and numerical techniques. The splay states are observed for very low values of the nonlinearity parameter, i.e., for maps which deviate very slightly from the shift map case. We also observe that depending on the parameters of the system the splay state bifurcates to a mixed or chimera splay state consisting of a mixture of splay and synchronized states, together with kinks in the phases of some of the maps and then to a stable globally synchronized state. We show that these pure states and the mixed states are all temporally chaotic for our systems, and we explore the stability of these states to perturbations. Our studies may provide pointers to the behavior of systems in diverse application contexts such as Josephson junction arrays and chemical oscillations.

Chimera states in coupled map lattices: Spatiotemporally intermittent behavior and an equivalent cellular automaton

Abstract: We construct an equivalent cellular automaton (CA) for a system of globally coupled sine circle maps with two populations and distinct values for intergroup and intragroup coupling. The phase diagram of the system shows that the coupled map lattice can exhibit chimera states with synchronized and spatiotemporally intermittent subgroups after evolution from random initial conditions in some parameter regimes, as well as to other kinds of solutions in other parameter regimes. The CA constructed by us reflects the global nature and the two population structure of the coupled map lattice and is able to reproduce the phase diagram accurately. The CA depends only on the total number of laminar and burst sites and shows a transition from co-existing deterministic and probabilistic behavior in the chimera region to fully probabilistic behavior at the phase boundaries. This identifies the characteristic signature of the transition of a cellular automaton to a chimera state. We also construct an evolution equation for the average number of laminar/burst sites from the CA, analyze its behavior and solutions, and correlate these with the behavior seen for the coupled map lattice. Our CA and methods of analysis can have relevance in wider contexts.

Classification and Analysis of Chimera States

Abstract: We study the existence of different types of chimera states in a globally coupled sine circle map lattice with different strengths of intergroup and intragroup coupling. Some of the typical chimera phase configurations that can be observed in this system are aperiodic chimera states, splay chimera states and chimera states with spatiotemporally intermittent behaviour in the desynchronised group. These states are seen in different regions of the parameter space for three distinct kinds of initial conditions. We obtain the phase diagram containing the third type of chimera state, viz. the one with spatiotemporally intermittent regions, using complex order parameters. We construct an equivalent cellular automaton (CA) and reproduce the phase diagram in the region of interest by solving the mean field equation obtained for the CA.

Probabilistic signatures of spatiotemporal intermittency in the coupled sine circle map lattice

Abstract: The phase diagram of the coupled sine circle map system exhibits a variety of interesting phenomena including spreading regions with spatiotemporal intermittency, non-spreading regions with spatial intermittency, and coherent structures termed solitons. A spreading to non-spreading transition is seen in the system. A cellular automaton version of the coupled system maps the spreading to non-spreading transition to a transition from a probabilistic to a deterministic cellular automaton. The solitonic sector of the system shows spatiotemporal intermittency with soliton creation, propagation and absorption. A probabilistic cellular automaton mapping is set up for this sector which can identify each one of these phenomena.

Invited Article: Mitigation of dynamical instabilities in laser arrays via non-Hermitian coupling

Abstract: Arrays of coupled semiconductor lasers are systems possessing complex dynamical behavior and are of major interest in photonics and laser science. Dynamical instabilities, arising from supermode competition and slow carrier dynamics, are known to prevent stable phase locking in a wide range of parameter space, requiring special methods to realize stable laser operation. Inspired by recent concepts of parity-time (PT) and non-Hermitian photonics, in this work, we consider non-Hermitian coupling engineering in laser arrays in a ring geometry and show, both analytically and numerically, that non-Hermitian coupling can help to mitigate the onset of dynamical laser instabilities. In particular, we consider in detail two kinds of nearest-neighbor non-Hermitian couplings: symmetric but complex mode coupling (type-I non-Hermitian coupling) and asymmetric mode coupling (type-II non-Hermitian coupling). Suppression of dynamical instabilities can be realized in both coupling schemes, resulting in stable phase-locking laser emission with the lasers emitting in phase (for type-I coupling) or with π/2 phase gradient (for type-II coupling), resulting in a vortex far-field beam. In type-II non-Hermitian coupling, chirality induced by asymmetric mode coupling enables laser phase locking even in the presence of moderate disorder in the resonance frequencies of the lasers.

Mitigation of dynamical instabilities in laser arrays via non-Hermitian coupling

Abstract: Arrays of coupled semiconductor lasers are systems possessing complex dynamical behavior that are of major interest in photonics and laser science. Dynamical instabilities, arising from supermode competition and slow carrier dynamics, are known to prevent stable phase locking in a wide range of parameter space, requiring special methods to realize stable laser operation. Inspired by recent concepts of parity-time ($\mathcal{PT}$) and non-Hermitian photonics, in this work we consider non-Hermitian coupling engineering in laser arrays in a ring geometry and show, both analytically and numerically, that non-Hermitian coupling can help to mitigate the onset of dynamical laser instabilities. In particular, we consider in details two kinds of nearest-neighbor non-Hermitian couplings: symmetric but complex mode coupling (type-I non-Hermitian coupling) and asymmetric mode coupling (type-II non-Hermitian coupling). Suppression of dynamical instabilities can be realized in both coupling schemes, resulting in stable phase-locking laser emission with the lasers emitting in phase (for type-I coupling) or with $\pi/2$ phase gradient (for type-II coupling), resulting in a vortex far-field beam. In type-II non-Hermitian coupling, chirality induced by asymmetric mode coupling enables laser phase locking even in presence of moderate disorder in the resonance frequencies of the lasers.

Noise and delay sustained chimera state in small world neuronal network

Abstract: Chimera state in neuronal network means the coexistence of synchronized and desynchronized firing patterns. It attracts much attention recently due to its possible relevance to the phenomenon of unihemispheric sleep in mammals. In this paper, we search for chimera state in a noisy small-world neuronal network, in which the neurons are delayed coupled. We found both transient and permanent chimera state when time delay is close to a critical value. The chimera state occurs due to the competition between the synchronized and desynchronized patterns in the neuronal network. On the other hand, intermediate intensity of noise facilitates the occurrence of delay-sustained chimera states. Comparison between noise and delay shows that time delay is the key factor determining the chimera state, whereas noise is a subordinate one.

Chimera States in a Ring of Nonlocally Coupled Oscillators

Abstract: Arrays of identical limit-cycle oscillators have been used to model a wide variety of pattern-forming systems, such as neural networks, convecting fluids, laser arrays, and coupled biochemical oscillators. These systems are known to exhibit rich collective behavior, from synchrony and traveling waves to spatiotemporal chaos and incoherence. Recently, Kuramoto and his colleagues reported a strange new mode of organization--here called the chimera state--in which coherence and incoherence exist side by side in the same system of oscillators. Such states have never been seen in systems with either local or global coupling; they are apparently peculiar to the intermediate case of nonlocal coupling. Here we give an exact solution for the chimera state, for a one-dimensional ring of phase oscillators coupled nonlocally by a cosine kernel. The analysis reveals that the chimera is born in a continuous bifurcation from a spatially modulated drift state, and dies in a saddle-node collision with an unstable version of itself.