arXiv subjects

Tanmoy Banerjee

Publications and source records attributed to Tanmoy Banerjee.

34 records · Page 2Linked to original sources

arXiv2017

Increased persistence via asynchrony in oscillating ecological populations with long-range interaction

Understanding the influence of structure of dispersal network on the species persistence and modeling a much realistic species dispersal in nature are two central issues in spatial ecology. A realistic dispersal structure which favors the persistence of interacting ecological systems has been studied in [Holland \& Hastings, Nature, 456:792--795 (2008)], where it is shown that a randomization of the structure of dispersal network in a metapopulation model of prey and predator increases the species persistence via clustering, prolonged transient dynamics, and amplitudes of population fluctuations. In this paper, by contrast, we show that a deterministic network topology in a metapopulation can also favor asynchrony and prolonged transient dynamics if species dispersal obeys a long-range interaction governed by a distance-dependent power-law. To explore the effects of power-law coupling, we take a realistic ecological model, namely the Rosenzweig-MacArthur model in each patch (node) of the network of oscillators, and show that the coupled system is driven from synchrony to asynchrony with an increase in the power-law exponent. Moreover, to understand the relationship between species persistence and variations in power-law exponent, we compute correlation coefficient to characterize cluster formation, synchrony order parameter and median predator amplitude. We further show that smaller metapopulations with less number of patches are more vulnerable to extinction as compared to larger metapopulations with higher number of patches. We believe that the present work improves our understanding of the interconnection between the random network and deterministic network in theoretical ecology.

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arXiv2016

Control of birhythmicity through conjugate self-feedback: Theory and experiment

Birhythmicity arises in several physical, biological and chemical systems. Although, many control schemes are proposed for various forms of multistability, only a few exist for controlling birhythmicity. In this paper we investigate the control of birhythmic oscillation by introducing a self-feedback mechanism that incorporates the variable to be controlled and its canonical conjugate. Using a detailed analytical treatment, bifurcation analysis and experimental demonstrations we establish that the proposed technique is capable of eliminating birhythmicity and generates monorhythmic oscillation. Further, the detailed parameter space study reveals that, apart from monorhythmicity, the system shows transition between birhythmicity and other dynamical forms of bistability. This study may have practical applications in controlling birhythmic behavior of several systems, in particular in biochemical and mechanical processes.

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arXiv2016

Generation and cessation of oscillations: Interplay of excitability and dispersal in a class of ecosystem

We investigate the complex spatiotemporal dynamics of an ecological network with species dispersal mediated via a mean-field coupling. The local dynamics of the network are governed by the Truscott--Brindley model, which is an important ecological model showing excitability. Our results focus on the interplay of excitability and dispersal by always considering that the individual nodes are in their (excitable) steady states. In contrast to the previous studies, we not only observe the dispersal induced generation of oscillation but we also report two distinct mechanisms of cessation of oscillations, namely amplitude and oscillation death. We show that, the dispersal between the nodes influences the intrinsic dynamics of the system resulting multiple oscillatory dynamics such as period-1 and period-2 limit cycles. We also show the existence of multi-cluster states which has much relevance and importance in ecology.

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arXiv2016

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.

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arXiv2016

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 {\it local}, synaptic {\it gradient} coupling. We discover a new chimera pattern, namely the {\it imperfect traveling chimera} where the incoherent traveling domain spreads into the coherent domain of the network. Remarkably, we also find that chimera states arise even for {\it 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; 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 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, in-phase synchronized state and global amplitude death state.

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arXiv2016

Environmental coupling in ecosystems: From oscillation quenching to rhythmogenesis

How do landscape fragmentation affects ecosystems diversity and stability is an important and complex question in ecology with no simple answer, as spatially separated habitats where species live are highly dynamic rather than just static. Taking into account the species dispersal among nearby connected habitats (or patches) through a common dynamic environment, we model the consumer-resource interactions with ring type coupled network. Characterizing the dynamics of consumer-resource interactions in a coupled ecological system with three fundamental mechanisms: such as the interaction within the patch, the interaction between the patch and the interaction through a common dynamic environment, we report the occurrence of various atypical collective behaviors. We show that, the interplay between dynamic environment and dispersal among connected patches exhibits the mechanism of generation of oscillations, i.e., rhythmogenesis, as well as suppression of oscillations, i.e., amplitude death and oscillation death. Also, the transition of homogeneous steady state to inhomogeneous steady state occurs through a co-dimension-2 bifurcation. Emphasizing a network of spatially extended system, the coupled model exposes the collective behavior of synchrony-stability relationship with various synchronization occurrences such as in-phase and out-of-phase.

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arXiv2015

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. Nature 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 {\it two control parameters}, namely the {\it density of the mean-field} and the {\it 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 an unique feature of this mean-field coupling that is not available in other coupling schemes. Finally, we report the {\it first} experimental observation of revival of oscillation from the mean-field--induced oscillation suppression state that supports our theoretical results.

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arXiv2015

Mixed mode oscillation suppression states in coupled oscillators

We report a new collective dynamical state, namely the {\it mixed mode oscillation suppression} state where different set of variables of a system of coupled oscillators show different types of oscillation suppression states. We identify two variants of it: The first one is a {\it mixed mode death} (MMD) state where a set of variables of a system of coupled oscillators show an oscillation death (OD) state, while the rest are in an amplitude death (AD) state under the identical parametric condition. In the second mixed death state (we refer it as the MNAD state) a nontrivial bistable AD and a monostable AD state appear simultaneously to different set of variables of a same system. We find these states in paradigmatic chaotic Lorenz system and Lorenz-like system under generic coupling schemes. We identify that while the reflection symmetry breaking is responsible for the MNAD state, the breaking of both the reflection and translational symmetries result in the MMD state. Using a rigorous bifurcation analysis we establish the occurrence of the MMD and MNAD states, and map their transition routes in parameter space. Moreover, we report the {\it first} experimental observation of the MMD and MNAD states that supports our theoretical results. We believe that this study will broaden our understanding of oscillation suppression states, subsequently, it may have applications in many real physical systems, such as laser and geomagnetic systems, whose mathematical models mimic the Lorenz system.

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arXiv2015

Chimera-Like Coexistence of Synchronized Oscillation and Death in an Ecological Network

We report a novel spatiotemporal state, namely the chimera-like incongruous coexistence of {\it synchronized oscillation} and {\it stable steady state} (CSOD) in a realistic ecological network of nonlocally coupled oscillators. Unlike the {\it chimera} and {\it chimera death} state, in the CSOD state identical oscillators are self-organized into two coexisting spatially separated domains: In one domain neighboring oscillators show synchronized oscillation and in another domain the neighboring oscillators randomly populate either a synchronized oscillating state or a stable steady state (we call it a death state). We show that the interplay of nonlocality and coupling strength results in two routes to the CSOD state: One is from a coexisting mixed state of amplitude chimera and death, and another one is from a globally synchronized state. We further explore the importance of this study in ecology that gives a new insight into the relationship between spatial synchrony and global extinction of species.

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arXiv2014

Transitions among the diverse oscillation quenching states induced by the interplay of direct and indirect coupling

We report the transitions among different oscillation quenching states induced by the interplay of diffusive (direct) coupling and environmental (indirect) coupling in coupled identical oscillators. This coupling scheme was introduced by Resmi {\it et al}. [Phys. Rev. E, 84, 046212 (2011)] as a general scheme to induce amplitude death (AD) in nonlinear oscillators. Using a detailed bifurcation analysis we show that in addition to AD, which actually occurs only in a small region of parameter space, this coupling scheme can induce other oscillation quenching states, namely oscillation death (OD) and a novel nontrvial AD (NAD) state, which is a nonzero {\it bistable} homogeneous steady state; more importantly, this coupling mediates a transition from AD to OD state and a new transition from AD to NAD state. We identify diverse routes to the NAD state and map all the transition scenarios in the parameter space for periodic oscillators. Finally, we present the first experimental evidence of oscillation quenching states and their transitions induced by the interplay of direct and indirect coupling.

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arXiv2014

Chimera death induced by the mean-field diffusive coupling

Recently a novel dynamical state, called the {\it chimera death}, is discovered in a network of non locally coupled identical oscillators [A. Zakharova, M. Kapeller, and E. Schöll, Phy.Rev.Lett. 112, 154101 (2014)], which is defined as the coexistence of spatially coherent and incoherent oscillation death state. This state arises due to the interplay of non locality and symmetry breaking and thus 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 non local 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.

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arXiv2014

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

We report the first 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, arXiv:1403.2907, 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.

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arXiv2014

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 {\it 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 {\it intrinsic time-delays} associated with the individual systems, and has no analogue in non-delayed systems or coupled oscillators with {\it 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.

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arXiv2014

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

We study the transition from amplitude death (AD) to 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 {\it identical} limit cycle oscillators. We identify a parameter region where OD and a novel {\it nontrivial} AD (NT-AD) state coexist. This NT-AD 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 but destroy this state. We extend our study to a network of mean-field coupled oscillators to show that the transition scenario preserves and the oscillators form a two cluster state.

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arXiv2013

Synchronization in hyperchaotic time-delayed electronic oscillators coupled indirectly via a common environment

The present paper explores the synchronization scenario of hyperchaotic time-delayed electronic oscillators coupled indirectly via a common environment. We show that depending upon the coupling parameters a hyperchaotic time-delayed system can show in-phase or complete synchronization, and also inverse-phase or anti-synchronization. This paper reports the first experimental confirmation of synchronization of hyperchaos in time-delayed electronic oscillators coupled indirectly through a common environment. We confirm the occurrence of in-phase and inverse-phase synchronization phenomena in the coupled system through the dynamical measures like generalized autocorrelation function, correlation of probability of recurrence, and the concept of localized sets computed directly from the experimental time-series data. We also present a linear stability analysis of the coupled system. The experimental and analytical results are further supported by the detailed numerical analysis of the coupled system. Apart from the above mentioned measures, we numerically compute another quantitative measure, namely, Lyapunov exponent spectrum of the coupled system that confirms the transition from the in-phase (inverse-phase) synchronized state to the complete (anti-) synchronized state with the increasing coupling strength.

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arXiv2012

Single amplifier biquad based inductor-free Chua's circuit

The present paper reports an inductor-free realization of Chua's circuit, which is designed by suitably cascading a single amplifier biquad based active band pass filter with a Chua's diode. The system has been mathematically modeled with three-coupled first-order autonomous nonlinear differential equations. It has been shown through numerical simulations of the mathematical model and hardware experiments, that the circuit emulates the behaviors of a classical Chua's circuit, e.g., fixed point behavior, limit cycle oscillation, period doubling cascade, chaotic spiral attractors, chaotic double scrolls and boundary crisis. The occurrence of chaotic oscillation has been established through experimental power spectrum, and quantified with the dynamical measure like Lyapunov exponents.

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