• Issue front cover thumbnail

      Volume 1, Issue 1

      December 2017,   pages  i-224

    • Organizing Commitee

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    • Editorial

      Durgadas P Kasbekar

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    • Foreword

      Hilda A Cerdeira Neelima Gupte Jürgen Kurths Ram Ramaswamy

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    • Personal perspectives in nonlinear science: Looking back, looking forward

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    • List of Participants

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    • How good are network centrality measures? Longitudinal analysis of traffic in a railway network in the United States


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      Transportation networks are plagued by frequent delays, which pose crucial challenges to the economic advancement of a country. In previous studies, transportation networks have been envisioned as network structures of vertices with links representing a connection between two vertices. In the present work, the focus is on the delay analysis using tools of complex network analysis of the Amtrak railway network in the US. The Amtrak delay data for a period of 6 years between 2009 and 2014 was analyzed. It was observed that delay distribution varied every year and also for same stations in different years. The effect of conventional network measures on the average daily departure delay at various stations and also on the total daily traffic load on the station were estimated. Contrary to the predictive power of network topology measures in model transportation networks, it was observed that the topology measures had a negligible effect on Amtrak delay, with stations that faced the highest traffic experiencing shorter average delays. The results of this study call for additional realistic network measures and routing schemes, which could capture the features of the real-world transportation networks.

      PACS Nos 89.40.-a

    • Dynamics of slow and fast systems on complex networks


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      We study the occurrence of frequency synchronized states with tunable emergent frequencies in a network of connected systems. This is achieved by the interplay between time scales of nonlinear dynamical systems connected to form a network, where out of N systems, m evolve on a slower time scale. In such systems, in addition to frequency synchronized states, we also observe amplitude death, synchronized clusters and multifrequency states. We report an interesting crossover behavior from fast to slow collective dynamics as the number of slow systems m increases. The transition to amplitude death is analyzed in detail for minimal network configurations of 3 and 4 systems which actually form possible motifs of the full network.

      PACS Nos 05.45.Yv; 05.45.Xt; 05.45.Gg; 89.75.Fb

    • Interpreting physical flows in networks as a communication system


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      Information theory concepts and methodologies constitute the background of how communication systems are studied and understood. They are focused mainly on the source-channel-receiver problem and on the asymptotic limits of accuracy and communication rates, which are the classical problems studied by Shannon. However, the impact of information theory on networks (acting as the channel) is just starting. Here, we present an approach to understand how information flows in any connected network. Our approach is based on defining linear conservative flows that travel through the network from single or multiple sources to receivers. With these flows, we define a transition probability matrix that is similar to a Markovian process. Consequently, this framework allows us to have an analytical description of the problem and also to link the topological invariants of the network, such as the node degree, with the information flow and capacity, namely, the maximum amount of information generated by the network for any source-receiver configuration. In particular, our approach is able to deal with information transmission in modular networks (networks containing community structures) or multiplex networks (networks with multiple layers), which are nowadays of paramount importance.

      PACS Nos 89.75.Hc; 45.30.+s; 02.50.-r; 41.20-q

    • Data assimilation with Chua’s circuit


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      Data assimilation refers to a set of techniques used to combine observational information with numerical models for chaotic dynamical systems and provides a rich interface between dynamical and statistical methodologies in nonlinear dynamics. The main aim of this paper is to compare and contrast two extensively studied paradigms in each of these approaches: on one hand, the ensemble Kalman filter which is a statistical estimation technique, and on the other hand, chaotic synchronization that has been studied in many other contexts, by viewing synchronization as a data assimilation method. In particular, we study the sensitivity of these two methods to changes in observational noise and observational frequency, using both simulated observations and data obtained from an experimental realization of a commonly used low-dimensional dynamical system, namely, Chua circuit, in both the periodic as well as the chaotic regime.

      PACS Nos 05.45.Xt; 05.45.Ac

    • RQA correlations on real business cycles time series


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      Trade cycles are complex phenomena which oscillate because of economic downturns and expansions. Recurrence quantification analysis (RQA) detects state changes without necessitating any a priori mathematical assumption and highlights hidden features of the dynamics both at equilibrium and near transition phases. This paper aims to understand some potential application of recurrence quantification analysis in detecting recessions.

      PACS Nos 05.10.-a; 05.45.Tp; 05.45.-a

    • Determining the minimum embedding dimension for state space reconstruction through recurrence networks


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      The analysis of observed time series from nonlinear systems is usually done by making a time-delay reconstruction to unfold the dynamics on a multidimensional state space. An important aspect of the analysis is the choice of the correct embedding dimension. The conventional procedure used for this is either the method of false nearest neighbors or the saturation of some invariant measure, such as, correlation dimension. Here we examine this issue from a complex network perspective and propose a recurrence network based measure to determine the acceptable minimum embedding dimension to be used for such analysis. The measure proposed here is based on the well known Kullback-Leibler divergence commonly used in information theory. We show that the measure is simple and direct to compute and give accurate result for short time series. To show the significance of the measure in the analysis of practical data, we present the analysis of two EEG signals as examples.

      PACS Nos 05.45.-a; 05.45 Tp; 89.75 Hc

    • Inferring interdependencies from short time series


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      Complex networks provide an invaluable framework for the study of interlinked dynamical systems. In many cases, such networks are constructed from observed time series by first estimating the interdependencies between pairs of datasets. However, most of the classic and state-of-the-art interdependence estimation techniques require sufficiently long time series for their successful application. In this study, we present a modification of the inner composition alignment approach (IOTA), correspondingly termed mIOTA, and review its advantages. Using two coupled auto-regressive stochastic processes, we demonstrate the discriminating power of mIOTA and show that it outperforms standard interdependence measures. We then use mIOTA to derive econo-climatic networks of interdependencies between economic indicators and climatic variability for Sub-Saharan Africa (AFR) and South Asia including India (SAS). Our analysis uncovers that crop production in AFR is strongly interdependent with the regional rainfall. While the gross domestic product (GDP) as an economic indicator in AFR is independent of climatic factors, we find that precipitation in the SAS influences the regional GDP, likely reflecting the influence of the summer monsoons. The differences in the interdependence structures between AFR and SAS reflect an underlying structural difference in their overall economies, as well as their agricultural sectors.

      PACS Nos 05.45.; 02.50.-r; 02.50.Tt; 05.45.Tp; 02.70.Rr; 93.30.Bz; 93.30.Db; 92.60.Ry; 92.70.Kb; 92.70.Mn; 89.65.Gh; 89.75.Fb

    • Nonlinear chaos-dynamical approach to analysis of atmospheric radon 222Rn concentration time series


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      We present the theoretical foundations of an effective universal complex chaos-dynamical approach to the analysis and prediction of atmospheric radon 222Rn concentration using the beta particle activity data of radon monitors (with a pair of Geiger–Muller counters). The approach presented consistently includes a number of new or improved available methods (correlation integral, fractal analysis, algorithms of average mutual information and false nearest neighbors, Lyapunov’s exponents, surrogate data, nonlinear prediction schemes, spectral methods, etc.) of modeling and analysis of atmospheric radon 222Rn concentration time series. We first present the data on the topological and dynamical invariants for the time series of the 222Rn concentration. Using the data measurements of the radon concentration time series at SMEAR II station of the Finnish Meteorological Institute, we found the elements of deterministic chaos.

      PACS Nos 05.45.+b; 42.50.Ne; 42.55.Px; 42.65.Pc

    • Flow dynamic study of a single-phase square NCL using recurrence plot and recurrence quantification


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      The cooling of a heat-generating system is one of the biggest concerns in the field of thermal engineering. Hence, the focus is on such cooling systems which do not involve any active components (passive systems) for high reliability and compact size. For this reason, in heat transfer, the natural circulation loop (NCL) is used extensively. NCL works as a cooling system by removing heat from a lower-elevation heat source and deposit the heat to a higher-elevation heat sink by the moving fluid present in it. As spontaneous dynamics of the working fluid plays a very important role in the performance of the system, it is necessary to study proper fluid flow dynamics. With increase in heater power, a change in loop fluid flow dynamics has been observed. For the comparatively low heater power, we observed steady flow, and with the increase in heater power first, we obtained the oscillatory flow, and then with the addition of more heater power, we observed flow reversal. In this study, we first investigated the instability associated with the loop fluid flow with the help of recurrence plot. Along with recurrence plot we also compute the recurrence quantification analysis. From the recurrence quantification analysis, we can predict early about the change in flow pattern from oscillatory region to flow-reversal region.

      PACS Nos: 05.60.-k

    • Structure of simplicial complexes of graphs representing magnetization-reversal time series


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      Mapping time series onto graphs and the use of graph theory methods opens up the possibility to study the structure of the phase space manifolds underlying the fluctuations of a dynamical variable. Here, we go beyond the standard graph measures and analyze the higher-order structures such as triangles, tetrahedra and higher-order cliques and their complexes present in the time-series networks, which are detectable by algebraic topology methods. We investigate the Barkhausen noise signal which accompanies domain-wall dynamics during magnetization reversal in weakly disordered ferromagnets by a slow increase of the external field along the hysteresis loop. Our analysis demonstrates how the appearance of the complexes with cliques of a high order correlates to the enhanced collective fluctuations in the central part of the hysteresis loop, where domain-wall depinning occurs. In contrast, the fractional Gaussian noise fluctuations at the beginning of the loop correspond to the graph of a simpler topology. The determined topology measures serve as geometrical indicators of changing dynamical regimes along the hysteresis loop. The multifractal analysis of the corresponding segments of the signal confirms that we deal with different types of stochastic processes.

      PACS Nos 12.60.Jv; 12.10.Dm; 98.80.Cq; 11.30.Hv

    • Nonlinearity in data with gaps: Application to ecological and meteorological datasets


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      Datagaps are ubiquitous in real-world observational data. Quantifying nonlinearity in data having gaps can be challenging. Reported research points out that interpolation can affect nonlinear quantifiers adversely, artificially introducing signatures of nonlinearity where none exist. In this paper we attempt to quantify the effect that datagaps have on the multifractal spectrum (f(α)) in the absence of interpolation. We identify tolerable gap ranges, where the measures defining the f(α) curve do not show considerable deviation from the evenly sampled case. We apply this to the multifractal spectra of multiple datasets with missing data from the SMEAR database. The datasets we consider include ecological datasets from SMEAR I, namely CO2 exchange variation, photosynthetically active radiation levels and soil moisture variation time series, and meteorological datasets from SMEAR II, namely dew point variation and air temperature variation. We could establish multifractality due to deterministic nonlinearity in two of these datasets, where the gaps were within tolerable limits.

      PACS Nos 05.45.–a; 05.45.Tp; 87.23.–n; 92.60.–e

    • Missing cycles: Effect of climate change on population dynamics


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      Explaining observations in the population dynamics of ecosystems influenced by the environment and being able to correctly predict future events in these complex systems is one of the major challenges in mathematical modelling. We present our models having climate parameters which explain experimental observations of the cyclic population dynamics of the larch budmoth – an insect pest which causes massive defoliation of entire larch forests at high altitudes around the world. The tritrophic ecological system consists of the larch trees, the budmoth and parasitoid species which live off the budmoths. We make an important modification of the models we had proposed earlier by incorporating a slow time dependence in one of the species-specific parameters, in order to provide an explanation for the irregular larch budmoth cyclic outbreaks observed in the French Alps.

      PACS Nos 05.45.-a; 05.45.Pq; 87.23.Cc

    • Temporal self-similar synchronization patterns and scaling in repulsively coupled oscillators


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      We study synchronization patterns in repulsively coupled Kuramoto oscillators and focus on the impact of disorder in the natural frequencies. Among other choices we select the grid size and topology in a way that we observe a dynamically induced dimensional reduction with a continuum of attractors as long as the natural frequencies are uniformly chosen. When we introduce disorder in these frequencies, we find limit cycles with periods that are orders of magnitude longer than the natural frequencies of individual oscillators. Moreover we identify sequences of temporary patterns of phase-locked motion, which are self-similar in time and whose periods scale with a power of the inverse width about a uniform frequency distribution. This behavior provides challenges for future research.

      PACS Nos 05.45-a; 05.45.Xt; 05.40.Ca; 05.90.+m

    • The charged bubble oscillator: Dynamics and thresholds


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      The nonlinear, forced oscillations of a bubble in a fluid due to an external pressure field are studied theoretically. In the presence of a constant charge on the bubble, the bubble oscillator’s behaviour changes markedly. We report results at significantly higher pressures and forcing frequencies than presented earlier. The influence of the bubble’s ambient radius on thresholds and dynamics is also reported. Charge and pressure thresholds are calculated for the system, delineating different dynamics.

      PACS Nos 05.45.-a; 05.90.+m

    • Chaos in three coupled rotators: From Anosov dynamics to hyperbolic attractors


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      Starting from Anosov chaotic dynamics of geodesic flow on a surface of negative curvature, we develop and consider a number of self-oscillatory systems including those with hinged mechanical coupling of three rotators and a system of rotators interacting through a potential function. These results are used to design an electronic circuit for generation of rough (structurally stable) chaos. Results of numerical integration of the model equations of different degrees of accuracy are presented and discussed. Also, circuit simulation of the electronic generator is provided using the NI Multisim environment. Portraits of attractors, waveforms of generated oscillations, Lyapunov exponents, and spectra are considered and found to be in good correspondence for the dynamics on the attractive sets of the self-oscillatory systems and for the original Anosov geodesic flow. The hyperbolic nature of the dynamics is tested numerically using a criterion based on statistics of angles of intersection of stable and unstable subspaces of the perturbation vectors at a reference phase trajectory on the attractor.

      PACS Nos 05.45.Ac; 84.30.-r; 02.40.Yy

    • Grad-type fourteen-moment theory for dilute granular gases


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      Grad’s moment method is applied to derive the system of fully nonlinear 14-moment equations for dilute granular gases. The derived system of 14-moment equations is solved analytically in a quasilinear setting to obtain the homogeneous cooling state solution, and it is shown that the nonlinear terms of scalar fourth moment have practically no effect on Haff’s law. The linear stability of the homogeneous cooling state is analyzed through the 14-moment system by decomposing it into two independent longitudinal and transverse problems. The eigenmodes for the longitudinal system are compared with those obtained by an existing theory by Kremer and Marques [12].

      PACS Nos 47.57.Gc; 51.10.+y; 47.45.Ab

    • Rate calculation in two-dimensional barriers with colored noise


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      The identification of an optimal dividing surface that is free of recrossings is the most important requirement for transition state theory to be exact. This task is particularly difficult in the presence of non-Markovian friction, i.e., colored noise forces. In this paper, we report a novel geometric method that circumvents the recrossing problem and is able to (i) identify reactive trajectories exactly, and (ii) compute reaction rates in a system with two degrees of freedom driven by non-Markovian friction. The extension of our method to higher dimensional systems is also discussed.

      PACS Nos 82.20.Db; 05.40.Ca; 05.45.2a; 34.10.+x

    • Dynamics of nonlinear oscillators with time-varying conjugate coupling


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      We explore the dynamical consequences of time-varying conjugate coupling in a system of nonlinear oscillators. We analyze the behavior of coupled systems with respect to the coupling switching frequency using normalized average synchronization error and average amplitude. We show that this form of time-varying interaction can induce an anomalous transition like the emergence of oscillation as well as the intermittent state with different dynamical states. This behavior is analyzed by numerical studies of specific cases of the Rössler oscillator and an ecological model of predator–prey systems.

      PACS Nos 05.45.Xt

    • Intermittency in delay-coupled FitzHugh–Nagumo oscillators and loss of phase synchrony as its precursor


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      We study the dynamical properties of in-out intermittency in a system of two identical FitzHugh–Nagumo oscillators coupled by multiple time delays. In this system, the intermittency is manifested as irregular switching between a nearly synchronous state with small and large amplitude chaotic oscillations and a highly asynchronous state with a single large amplitude oscillation. We show that loss of phase synchrony significantly prior to the occurrence of the asynchronous large amplitude oscillation can be used as a precursor to the switching of states in such systems.

      PACS Nos 05.45.-a

    • Coexistence of attractors in a coupled nonlinear delayed system modelling El Niño Southern Oscillations


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      We studied the dynamics of the sea surface temperature (SST) anomaly using a model of the temporal patterns of two sub-regions, mimicking behaviour similar to El Niño Southern Oscillations (ENSO). Specifically, we present the existence, stability, and basins of attraction of the solutions arising in the model system in the space of these parameters: self-delay, delay and inter-region coupling strengths. The emergence or suppression of oscillations in our models is a dynamical feature of utmost relevance, as it signals the presence or absence of ENSO-like oscillations. In contrast to the well-known low-order model of ENSO, where the influence of the neighbouring regions on the region of interest is modelled as external noise, we considered neighbouring regions as a coupled deterministic dynamical systems. Different parameters yielded a rich variety of dynamical patterns in our model, ranging from steady states and homogeneous oscillations to irregular oscillations and coexistence of oscillatory attractors, without explicit inclusion of noise. Interestingly, if we take the self-delay coupling strengths of the two sub-regions to be such that the temperature of one region goes to a fixed point regime when uncoupled, while the other system is in the oscillatory regime, then on coupling, both systems show oscillations. This implies that oscillations may arise in certain sub-regions through coupling to neighbouring regions. Namely, a sub-region with very low delay, which would naturally go to a steady state when uncoupled, yields oscillations when coupled to another sub-region with high enough delay. We explicitly obtained the basins of attraction for the different steady states and oscillatory states in the model. Our result might be helpful for forecasting of El Niño (or La Niña) progress, as it indicates the combination of initial SST anomalies in the sub-regions that can result in a El Niño/La Niña episodes. In particular, the result suggests using an interval as a criterion to estimate the El Niño or La Niño progress instead of the currently used the single value criterion.

      PACS Nos 92.10.-c; 05.45.-a

    • Chimera-like states generated by large perturbation of synchronous state of coupled metronomes


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      Chimera states in systems of coupled identical oscillators are spatiotemporal patterns in which different groups of oscillators can exhibit coexisting synchronous and incoherent behaviors despite homogeneous coupling. Here, considering the network of coupled pendula, we find that the patterns of chimera-like states can be generated after the large perturbation (in which one or a few oscillators have been stopped for the moment) of the synchronous state of the whole network. We show that these chimera-like states can be observed in simple experiments with mechanical oscillators, which are controlled by elementary dynamical equations given by classical mechanics.

      PACS Nos: 05.45.Xt

    • Spatial splay states in coupled map lattices and Josephson junction arrays


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      We show the existence and stability of frozen splay states as well as temporally chaotic splay states in a 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 circle maps which deviate very slightly from the shift map case. We also observe that, depending on the parameters of the system, the splay states bifurcate to mixed or chimera splay states, consisting of a mixture of splay and synchronised states, together with kinks in the phases of some of the maps and then to a globally synchronised state. We estimate the parameter regions where these pure states and the mixed states are seen. We also briefly show that similar spatial splay structures can exist in experimentally realisable systems like Josephson junction arrays and Hartley-like oscillator arrays.

      PACS Nos 12.60.Jv; 12.10.Dm; 98.80.Cq; 11.30.Hv

    • Synchronization, phase slips, and coherent structures in area-preserving maps


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      The problem of synchronization of coupled Hamiltonian systems exhibits interesting features due to the non-uniform or mixed nature (regular and chaotic) of the phase space. We study these features by investigating the synchronization of unidirectionally coupled area-preserving maps coupled by the Pecora–Carroll method. We find that coupled standard maps show complete synchronization for values of the nonlinearity parameter at which regular structures are still present in phase space. The distribution of synchronization times has a power law tail indicating long synchronization times for at least some of the synchronizing trajectories. With the introduction of coherent structures using parameter perturbation in the system, this distribution crosses over to exponential behavior, indicating shorter synchronization times, and the number of initial conditions which synchronize increases significantly, indicating an enhancement in the basin of synchronization. On the other hand, coupled blinking vortex maps display both phase synchronization and phase slips, depending on the location of the initial conditions. We discuss the implication of our results.

      PACS Nos 05.45.+b

    • Dynamic localization in walking droplets?


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      In this paper we explore the possibility of localization in the dynamics of walking droplets on a vertically vibrated liquid surface in the presence of a chaotic external potential and the limit of low memory, i.e., considering the effect of the wave generated only in the last bounce. Taking into account the similarity existing between this macroscopic system and de Broglie’s pilot wave theory, this study aims at establishing manifestations of chaos in the latter theory.

      PACS Nos 47.55.D; 47.85.g; 03.65.Sq

    • Transport in ratchets with single-file constraint


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      Diffusion of particles in restricted geometries is a subject of considerable interest due to their applicability in the observation and manipulation of nanoscopic systems. The single-file model has been introduced to model situations where the particles are constrained to move in nanopores in a single file without the chance for a particle exchange. Similarly, the motion of Brownian particles moving in a ratchet potential has been an active area of research because of its applicability to a wide range of nanoscale systems, including the transport properties of molecular motors. Here, we briefly review these models and discuss particle motion in a ratchet model constrained with the single-file condition. The motion of overdamped particles in a single-file model constrained to move in a ratchet potential is subdiffusive with mean square displacement that has t12 time dependence when hard-core interaction is significant, and becomes diffusive for long times. The N-particle switching time for maximum current is N times the switching time for one particle maximum current.

      PACS Nos 87.15.Aa, 87.15.Vv, 05.60.Cd, 05.45.Ac

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