Tanmoy Banerjee

Imperfect traveling chimera states induced by local synaptic gradient coupling.

In this paper, we report the occurrence of chimera patterns in a network of neuronal oscillators, which are coupled through local, synaptic gradient coupling. We discover a new chimera pattern, namely the imperfect traveling chimera state, where the incoherent traveling domain spreads into the coherent domain of the network. Remarkably, we also find that chimera states arise even for one-way local coupling, which is in contrast to the earlier belief that only nonlocal, global, or nearest-neighbor local coupling can give rise to chimera state; this find further relaxes the essential connectivity requirement of getting a chimera state. We choose a network of identical bursting Hindmarsh-Rose neuronal oscillators, and we show that depending upon the relative strength of the synaptic and gradient coupling, several chimera patterns emerge. We map all the spatiotemporal behaviors in parameter space and identify the transitions among several chimera patterns, an in-phase synchronized state, and a global amplitude death state.

Transition from amplitude to oscillation death under mean-field diffusive coupling.

We study the transition from the amplitude death (AD) to the oscillation death (OD) state in limit-cycle oscillators coupled through mean-field diffusion. We show that this coupling scheme can induce an important transition from AD to OD even in identical limit cycle oscillators. We identify a parameter region where OD and a nontrivial AD (NTAD) state coexist. This NTAD state is unique in comparison with AD owing to the fact that it is created by a subcritical pitchfork bifurcation and parameter mismatch does not support this state, but destroys it. We extend our study to a network of mean-field coupled oscillators to show that the transition scenario is preserved and the oscillators form a two-cluster state.

Mean-field-diffusion–induced chimera death state

Recently a novel dynamical state, called the chimera death, has been discovered in a network of nonlocally coupled identical oscillators (Zakharova A., Kapeller M. and Scholl E., Phys. Rev. Lett., 112 (2014) 154101), which is defined as the coexistence of spatially coherent and incoherent oscillation death state. This state arises due to the interplay of nonlocality and symmetry breaking and thus it bridges the gap between two important dynamical states, namely the chimera and oscillation death. In this paper we show that the chimera death can be induced in a network of generic identical oscillators with mean-field diffusive coupling and thus we establish that a nonlocal coupling is not essential to obtain chimera death. We identify a new transition route to the chimera death state, namely the transition from in-phase synchronized oscillation to chimera death via global amplitude death state. We ascribe the occurrence of chimera death to the bifurcation structure of the network in the limiting condition and show that multi-cluster chimera death states can be achieved by a proper choice of initial conditions.

Experimental observation of a transition from amplitude to oscillation death in coupled oscillators.

We report the experimental evidence of an important transition scenario, namely the transition from amplitude death (AD) to oscillation death (OD) state in coupled limit cycle oscillators. We consider two Van der Pol oscillators coupled through mean-field diffusion and show that this system exhibits a transition from AD to OD, which was earlier shown for Stuart-Landau oscillators under the same coupling scheme [T. Banerjee and D. Ghosh, Phys. Rev. E 89, 052912 (2014)]. We show that the AD-OD transition is governed by the density of mean-field and beyond a critical value this transition is destroyed; further, we show the existence of a nontrivial AD state that coexists with OD. Next, we implement the system in an electronic circuit and experimentally confirm the transition from AD to OD state. We further characterize the experimental parameter zone where this transition occurs. The present study may stimulate the search for the practical systems where this important transition scenario can be observed experimentally.

Amplitude death and synchronized states in nonlinear time-delay systems coupled through mean-field diffusion

We explore and experimentally demonstrate the phenomena of amplitude death (AD) and the corresponding transitions through synchronized states that lead to AD in coupled intrinsic time-delayed hyperchaotic oscillators interacting through mean-field diffusion. We identify a novel synchronization transition scenario leading to AD, namely transitions among AD, generalized anticipatory synchronization (GAS), complete synchronization (CS), and generalized lag synchronization (GLS). This transition is mediated by variation of the difference of intrinsic time-delays associated with the individual systems and has no analogue in non-delayed systems or coupled oscillators with coupling time-delay. We further show that, for equal intrinsic time-delays, increasing coupling strength results in a transition from the unsynchronized state to AD state via in-phase (complete) synchronized states. Using Krasovskii-Lyapunov theory, we derive the stability conditions that predict the parametric region of occurrence of GAS, GLS, and CS; also, using a linear stability analysis, we derive the condition of occurrence of AD. We use the error function of proper synchronization manifold and a modified form of the similarity function to provide the quantitative support to GLS and GAS. We demonstrate all the scenarios in an electronic circuit experiment; the experimental time-series, phase-plane plots, and generalized autocorrelation function computed from the experimental time series data are used to confirm the occurrence of all the phenomena in the coupled oscillators.

Revival of oscillation from mean-field-induced death: Theory and experiment

The revival of oscillation and maintaining rhythmicity in a network of coupled oscillators offer an open challenge to researchers as the cessation of oscillation often leads to a fatal system degradation and an irrecoverable malfunctioning in many physical, biological, and physiological systems. Recently a general technique of restoration of rhythmicity in diffusively coupled networks of nonlinear oscillators has been proposed in Zou et al. [Nat. Commun. 6, 7709 (2015)], where it is shown that a proper feedback parameter that controls the rate of diffusion can effectively revive oscillation from an oscillation suppressed state. In this paper we show that the mean-field diffusive coupling, which can suppress oscillation even in a network of identical oscillators, can be modified in order to revoke the cessation of oscillation induced by it. Using a rigorous bifurcation analysis we show that, unlike other diffusive coupling schemes, here one has two control parameters, namely the density of the mean-field and the feedback parameter that can be controlled to revive oscillation from a death state. We demonstrate that an appropriate choice of density of the mean field is capable of inducing rhythmicity even in the presence of complete diffusion, which is a unique feature of this mean-field coupling that is not available in other coupling schemes. Finally, we report the experimental observation of revival of oscillation from the mean-field-induced oscillation suppression state that supports our theoretical results.

THEORY AND EXPERIMENT OF A FIRST-ORDER CHAOTIC DELAY DYNAMICAL SYSTEM

We report the theory and experiment of a new time-delayed chaotic (hyperchaotic) system with a single scalar time delay and a nonlinearity described by a closed form mathematical function. Detailed stability and bifurcation analyses establish that with the suitable delay and system parameters, the system shows a stable limit cycle through a supercritical Hopf bifurcation. Numerical simulations exemplify that the system depicts mono-scroll and double-scroll chaos and hyperchaos for a range of delay and other system parameters. Nonlinear behavior of the system is characterized by Lyapunov exponents and Kaplan–Yorke dimension. It is established that, for some suitably chosen system parameters, the system shows hyperchaos even for a small or moderate time delay. Finally, the system is implemented in an analogue electronic circuit using off-the-shelf circuit elements. It is shown that the behavior of the time delay chaotic electronic circuit qualitatively agrees well with our analytical and numerical results.

A new dynamic gain control algorithm for speed enhancement of digital-phase locked loops (DPLLs)

A dynamic gain modification algorithm of a class of DPLLs has been proposed to improve its transient characteristics and tracking behavior. In this technique, rather taking a time invariant gain, the gain of the loop digital filter is made a function of the sampled value of the signal at every sampling instant. It has been shown analytically as well as numerically that the new structure is faster than the conventional one in its acquisition time and at the same time, it has a broader acquisition range.

Chaos, intermittency and control of bifurcation in a ZC2-DPLL

Nonlinear dynamics of a dual sampler-based zero crossing digital phase lock loop (ZC2-DPLL) has been investigated. Analysis supported by detailed numerical studies shows that the system enters a chaotic state through a cascade of period doubling bifurcation. The dynamics of the system have been quantified with the dynamical measures of Lyapunov exponent and correlation dimension. Further, it has been found that for certain system parameters intermittency occurs in the system. The occurrence of intermittency has been proved using the Pomeau–Manneville principle. The phenomenon of bifurcation control in a ZC2-DPLL using time delay feedback has been explored. It has been found that for some suitably chosen control parameters bifurcation phenomena can be controlled such that the stable locked zone of a bifurcation controlled ZC2-DPLL can be extended, which enhances the application potentiality of a ZC2-DPLL.

Chimera patterns induced by distance-dependent power-law coupling in ecological networks.

This paper reports the occurrence of several chimera patterns and the associated transitions among them in a network of coupled oscillators, which are connected by a long-range interaction that obeys a distance-dependent power law. This type of interaction is common in physics and biology and constitutes a general form of coupling scheme, where by tuning the power-law exponent of the long-range interaction the coupling topology can be varied from local via nonlocal to global coupling. To explore the effect of the power-law coupling on collective dynamics, we consider a network consisting of a realistic ecological model of oscillating populations, namely the Rosenzweig-MacArthur model, and show that the variation of the power-law exponent mediates transitions between spatial synchrony and various chimera patterns. We map the possible spatiotemporal states and their scenarios that arise due to the interplay between the coupling strength and the power-law exponent.