arXiv subjects

R. Suresh

Publications and source records attributed to R. Suresh.

At least 19 recordsLinked to original sources

arXiv2026

Delay-Controlled Heterogeneous Nucleation in Adaptive Dynamical Networks

Phase transitions constitute fundamental mechanisms underlying abrupt or qualitative changes in the collective dynamics of interacting units across a wide range of natural and engineered systems. In dynamical networks, such transitions lead to significant reorganization in the coordinated behavior of coupled elements. In adaptive dynamical networks, the connectivity evolves dynamically in response to the states of the nodes, resulting in a coevolution of structure and dynamics. In this work, we report two distinct forms of heterogeneous nucleation that give rise to single-step and multi-step phase transitions toward global synchronization in finite-size adaptive networks with connection delays. We demonstrate that the nature of the nucleation transition is governed by both the presence and magnitude of the delay, as well as the class of natural frequency distribution. Using a collective coordinate framework, we develop a mean-field description of cluster dynamics and derive an analytical upper bound condition for the existence of two-cluster states, which shows excellent agreement with numerical simulations. Furthermore, we extend the analysis to systems with distributed delays and obtain corresponding analytical conditions. Our results provide a theoretical framework for understanding synchronization transitions in adaptive networks with time-delayed interactions.

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arXiv2026

Frustration-Induced Collective Dynamical States in Pulse-Coupled Adaptive Winfree Networks

We investigate collective dynamics in a pulse-coupled adaptive Winfree network under the influence of a frustration (phase-lag) parameter. The coupling strengths coevolve according to a Hebbian adaptation rule and self-organize to support a wide variety of collective states. We observe frequency-clustered states, entrainment, bump states, bump--frequency cluster states, antipodal and multi-antipodal cluster states, chimera states, and incoherent dynamics. Notably, we report for the first time the spontaneous emergence of entrainment, bump, and bump--frequency cluster states in an adaptive network {\it without} any external forcing. To systematically characterize these regimes, we introduce three complementary measures of incoherence based on (i) time-averaged frequencies, (ii) instantaneous phases, and (iii) mean frequencies per bin. These measures enable the construction of one- and two-parameter phase diagrams that clearly delineate transitions between distinct dynamical states. Furthermore, we analytically derive the stability condition for the frequency-entrained state, which shows excellent agreement with numerical simulations. Our results highlight the crucial role of frustration-mediated plasticity in shaping rich self-organized dynamics in pulse-coupled adaptive networks.

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arXiv2026

Emergence of solitary and chimera states in adaptive pendulum networks under diverse learning rules

We investigate the interplay between phase lag and adaptive learning rules in a network of identical pendulum oscillators, where the coupling strengths evolve dynamically in response to the oscillators' states. Specifically, we examine two biologically inspired adaptation mechanisms, Hebbian and spike-timing-dependent plasticity (STDP), and their influence on the emergence of collective dynamical patterns. Under Hebbian adaptation, the network exhibits a wide range of organized behaviors, including two-cluster, solitary, multi-antipodal, and chimera states. In contrast, STDP coupling induces splay, splay-cluster, and splay-chimera configurations. Importantly, we find that the solitary state arises spontaneously in this adaptive network without requiring delays, nonlocal coupling, or external perturbations; instead, it is induced purely by variations in the phase-lag parameter. To the best of our knowledge, such delay-free and symmetry-preserving emergence of solitary behavior has not been reported previously in adaptive oscillator systems. To systematically characterize the resulting dynamical transitions, we employ two complementary incoherence measures based on the local standard deviation of (i) time-averaged frequencies and (ii) instantaneous phases across spatial bins, enabling the construction of detailed two-parameter phase diagrams. Analytical stability analysis of the two-cluster state shows strong agreement with numerical simulations, revealing regions of pronounced multistability. These findings establish adaptive pendulum networks as a minimal yet powerful framework for studying self-organized synchronization, chimera formation, and multistable transitions driven by diverse adaptation mechanisms.

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arXiv2025

Heterogeneous noise-induced extreme events and synchronization in a globally coupled network of FitzHugh-Nagumo oscillators

This study investigates the dynamics of a globally coupled network of heterogeneous FitzHugh Nagumo (FHN) oscillators under stochastic influences, with particular emphasis on the emergence of extreme events (EE). While previous studies explored FHN networks subjected to homogeneous noise, revealing behaviors such as noise-induced synchronization, stochastic resonance, and coherence resonance, the impact of noise heterogeneity remains poorly understood. Moreover, the emergence of EE under heterogeneous stochastic excitation has largely been overlooked. To address these gaps, we capture the natural variability in neuronal responses to external stimuli by introducing nonidentical noise sources, thereby reflecting diversity across the network. Our results reveal that EE can arise both globally, where large excursions occur collectively across the entire network, and partially, where only a subset of oscillators exhibits extreme activity depending on the interplay between noise intensity and coupling strength. We further identify three distinct classes of EE that enrich the system's dynamical repertoire and propose a quantitative metric capable of distinguishing between global and local occurrences. Remarkably, we demonstrate that even under heterogeneous noise inputs, noise can synchronize EE across the network, underscoring the robustness of collective dynamics in stochastic regimes. Furthermore, causal interaction analysis between oscillator pairs provides mechanistic insights into the initiation and propagation of EE. To the best of our knowledge, this constitutes the first demonstration of both partially and globally synchronized EE triggered solely by noise in a network of coupled oscillators. These findings enhance our understanding of noise-driven collective behavior in complex systems and provide new insights into neuronal dynamics under random influences.

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arXiv2025

Multivariate time series prediction using clustered echo state network

Many natural and physical processes can be understood by analyzing multiple system variables evolving, forming a multivariate time series. Predicting such time series is challenging due to the inherent noise and interdependencies among variables. Echo state networks (ESNs), a class of Reservoir Computing (RC) models, offer an efficient alternative to conventional recurrent neural networks by training only the output weights while keeping the reservoir dynamics fixed, reducing computational complexity. We propose a clustered ESNs (CESNs) that enhances the ability to model and predict multivariate time series by organizing the reservoir nodes into clusters, each corresponding to a distinct input variable. Input signals are directly mapped to their associated clusters, and intra-cluster connections remain dense while inter-cluster connections are sparse, mimicking the modular architecture of biological neural networks. This architecture improves information processing by limiting cross-variable interference and enhances computational efficiency through independent cluster-wise training via ridge regression. We further explore different reservoir topologies, including ring, Erd\H{o}s-R\'enyi (ER), and scale-free (SF) networks, to evaluate their impact predictive performance. Our algorithm works well across diverse real-world datasets such as the stock market, solar wind, and chaotic R\"ossler system, demonstrating that CESNs consistently outperform conventional ESNs in terms of predictive accuracy and robustness to noise, particularly when using ER and SF topologies. These findings highlight the adaptability of CESNs for complex, multivariate time series forecasting.

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arXiv2025

Noise induced extreme events in single Fitzhugh-Nagumo oscillator

The FitzHugh-Nagumo (FHN) model serves as a fundamental neuronal model which is extensively studied across various dynamical scenarios, we explore the dynamics of a scalar FHN oscillator under the influence of white noise. Unlike previous studies, in which extreme events (EE) were observed solely in coupled FHN oscillators, we demonstrate that a single system can exhibit EE induced by noise. Perturbation of the deterministic model in its steady state by random fluctuations reveals the emergence of subthreshold/small-amplitude oscillations (SAO), eventually leading to rare and extreme large-amplitude oscillations (LAO), which become particularly evident at minimal noise intensities. We elucidate the route by which these EE emerge, confirming their occurrence through probability calculations of trajectories in phase space. Additionally, our investigation reveals bursting phenomena in the system, which are characterized by specific levels of noise amplitude and elucidated using inter-spike interval statistics. At higher noise amplitudes, frequent LAO production is observed and attributed to self-induced stochastic resonance. The emergence of EE is explained through the theory of large fluctuations, with the escape rates of trajectories estimated via both analytical and numerical approaches. This study is significant because it reveals EE and bursting phenomena in a single FHN oscillator, offering potential new insights into the dynamics of neuronal populations.

cond-mat.dis-nn↗

arXiv2024

Extreme events in the Lienard system with asymmetric potential: An in-depth exploration

This research investigates the dynamics of a forced Lienard oscillator featuring asymmetric potential wells. We provide compelling evidence of extreme events (EE) in the system by manipulating the height of the potential well. In the case of a symmetric well, the system exhibits chaotic behavior, with the trajectory irregularly traversing between the two wells, resulting in frequent large oscillations under specific parameter values. However, the introduction of asymmetry in the potential wells induces a noteworthy transformation. The frequency of jumping between wells is significantly diminished. In essence, the system trajectory displays rare yet recurrent hops to the adjacent well, which we identify as EE. The intricate dynamical behavior observed in the system is elucidated through bifurcation diagrams and Lyapunov exponents. The emergence of EE in the system, governed by various parameters, is characterized using the threshold height, probability distribution function, and inter-event intervals. We illustrate the regions of EE using phase diagram plots and demonstrate the control of EE by incorporating a damping term into the system.

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arXiv2022

Extreme bursting events via pulse-shaped explosion in mixed Rayleigh-Lienard nonlinear oscillator

We study the dynamics of a parametrically and externally driven Rayleigh-Lienard hybrid model and report the emergence of extreme bursting events due to a novel pulse-shaped explosion mechanism. The system exhibits complex periodic and chaotic bursting patterns amid small oscillations as a function of excitation frequencies. In particular, the advent of rare and recurrent chaotic bursts that emerged for certain parameter regions is characterized as extreme events. We have identified that the appearance of a sharp pulse-like transition that occurred in the equilibrium points of the system is the underlying mechanism for the development of bursting events. Further, the controlling aspect of extreme events is attempted by incorporating a linear damping term, and we show that for sufficiently strong damping strength, the extreme events are eliminated from the system, and only periodic bursting is feasible.

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arXiv2021

Dynamics of coupled modified Rossler oscillators: the role of nonisochronicity parameter

The amplitude-dependent frequency of the oscillations, termed \emph{nonisochronicity}, is one of the essential characteristics of nonlinear oscillators. In this paper, the dynamics of the Rossler oscillator in the presence of nonisochronicity is examined. In particular, we explore the appearance of a new fixed point and the emergence of a coexisting limit-cycle and quasiperiodic attractors. We also describe the sequence of bifurcations leading to synchronized, desynchronized attractors and oscillation death states in the coupled Rossler oscillators as a function of the strength of nonisochronicity and coupling parameters. Further, we characterize the multistability of the coexisting attractors by plotting the basins of attraction. Our results open up the possibilities of understanding the emergence of coexisting attractors, and into a qualitative change of the collective states in coupled nonlinear oscillators in the presence of nonisochronicity.

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arXiv2020

Influence of dissipation on extreme oscillations of a forced anharmonic oscillator

Dynamics of a periodically forced anharmonic oscillator (AO) with cubic nonlinearity, linear damping, and nonlinear damping, is studied. To begin with, the authors examine the dynamics of an AO. Due to this symmetric nature, the system has two neutrally stable elliptic equilibrium points in positive and negative potential-wells. Hence, the unforced system can exhibit both single-well and double-well periodic oscillations depending on the initial conditions. Next, the authors include nonlinear damping into the system. Then, the symmetry of the system is broken instantly and the stability of the two elliptic points is altered to result in stable focus and unstable focus in the positive and negative potential-wells, respectively. Consequently, the system is dual-natured and is either non-dissipative or dissipative, depending on location in the phase space. Furthermore, when one includes a periodic external forcing with suitable parameter values into the nonlinearly damped AO system and starts to increase the damping strength, the symmetry of the system is not broken right away, but it occurs after the damping reaches a threshold value. As a result, the system undergoes a transition from double-well chaotic oscillations to single-well chaos mediated through extreme events (EEs). Furthermore, it is found that the large-amplitude oscillations developed in the system are completely eliminated if one incorporates linear damping into the system. The numerically calculated results are in good agreement with the theoretically obtained results on the basis of Melnikov's function. Further, it is demonstrated that when one includes linear damping into the system, this system has a dissipative nature throughout the entire phase space of the system. This is believed to be the key to the elimination of EEs.

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arXiv2020

Parametric excitation induced extreme events in MEMS and Lienard oscillator

The two paradigmatic nonlinear oscillatory models with parametric excitation are studied. The authors provide theoretical evidence for the appearance of extreme events (EEs) in those systems. First, the authors consider a well known Lienard type oscillator that shows the emergence of EEs via two bifurcation routes: Intermittency and period-doubling routes for two different critical values of the excitation frequency. The authors also calculate the return time of two successive EEs, defined as inter-event intervals, that follow Poisson-like distribution, confirm the rarity of the events. Further, the total energy of the Lienard oscillator is estimated to explain the mechanism for the development of EEs. Next, the authors confirmed the emergence of EEs in a parametrically excited microelectromechanical system. In this model, EEs occur due to the appearance of stick-slip bifurcation near the discontinuous boundary of the system. Since the parametric excitation is encountered in several real-world engineering models, like macro and micromechanical oscillators, the implications of the results presented in this paper are perhaps beneficial to understand the development of EEs in such oscillatory systems.

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arXiv2016

Emergence of a common generalized synchronization manifold in network motifs of structurally different time-delay systems

We point out the existence of a transition from partial to global generalized synchronization (GS) in symmetrically coupled structurally different time-delay systems of different orders using the auxiliary system approach and the mutual false nearest neighbor method. The present authors have recently reported that there exists a common GS manifold even in an ensemble of structurally nonidentical scalar time-delay systems with different fractal dimensions and shown that GS occurs simultaneously with phase synchronization (PS). In this paper we confirm that the above result is not confined just to scalar one-dimensional time-delay systems alone but there exists a similar type of transition even in the case of time-delay systems with different orders. We calculate the maximal transverse Lyapunov exponent to evaluate the asymptotic stability of the complete synchronization manifold of each of the main and the corresponding auxiliary systems, which in turn ensures the stability of the GS manifold between the main systems. Further we estimate the correlation coefficient and the correlation of probability of recurrence to establish the relation between GS and PS. We also calculate the mutual false nearest neighbor parameter which doubly confirms the occurrence of the global GS manifold.

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arXiv2015

Emergence of coexisting coherence and incoherence by an external forcing

A common external forcing can cause a saddle-node bifurcation in an ensemble of identical Duffing oscillators by breaking the symmetry of the individual bistable (double-well) unit. The strength of the forcing determines the separation between the saddle and node, which in turn dictates different dynamical transitions depending on the distribution of the initial states of the oscillators. In particular, chimera-like states appear in the vicinity of the saddle-node bifurcation for which theoretical explanation is provided from the stability of slow-scale dynamics of the original system of equations. Further, as a consequence, it is shown that even a linear nearest neighbor coupling can lead to the manifestation of the chimera states in an ensemble of identical Duffing oscillators in the presence of the common external forcing.

nlin.CD↗

arXiv2014

Dynamic environment coupling induce synchronized states in coupled time-delayed electronic circuits

We experimentally demonstrate the occurrence of various synchronized states in coupled piece-wise linear time-delayed electronic circuits using dynamic environment coupling where the environment has its own intrinsic dynamics via feedback from the circuits. We carry out these experiments in two different coupling configurations, namely mutual and subsystem coupling configurations. Depending upon the coupling strength and the nature of feedback, we observe a transition from nonsynchronization to complete synchronization via phase synchronization and from nonsynchronization to inverse synchronization via inverse-phase synchronization between the circuits in hyperchaotic regime. Snapshots of the time evolution, phase projection plots and localized sets of the circuits as observed experimentally from the oscilloscope, along with supporting numerical simulations confirm the existence of different synchronized states. Further, the transition to different synchronized states can be verified from the changes in the largest Lyapunov exponents, Correlation of Probability of Recurrence and Correlation Coefficient as a function of the coupling strength. We present a detailed linear stability analysis and obtain conditions for different synchronized states.

nlin.CD↗

arXiv2013

Global generalized synchronization in networks of different time-delay systems

We show that global generalized synchronization (GS) exists in structurally different time-delay systems, even with different orders, with quite different fractal (Kaplan-Yorke) dimensions, which emerges via partial GS in symmetrically coupled regular networks. We find that there exists a smooth transformation in such systems, which maps them to a common GS manifold as corroborated by their maximal transverse Lyapunov exponent. In addition, an analytical stability condition using the Krasvoskii-Lyapunov theory is deduced. This phenomenon of GS in strongly distinct systems opens a new way for an effective control of pathological synchronous activity by means of extremely small perturbations to appropriate variables in the synchronization manifold.

nlin.CD↗

arXiv2013

Zero-lag synchronization in coupled time-delayed piecewise linear electronic circuits

We investigate and report an experimental confirmation of zero-lag synchronization (ZLS) in a system of three coupled time-delayed piecewise linear electronic circuits via dynamical relaying with different coupling configurations, namely mutual and subsystem coupling configurations. We have observed that when there is a feedback between the central unit (relay unit) and at least one of the outer units, ZLS occurs in the two outer units whereas the central and outer units exhibit inverse phase synchronization (IPS). We find that in the case of mutual coupling configuration ZLS occurs both in periodic and hyperchaotic regimes, while in the subsystem coupling configuration it occurs only in the hyperchaotic regime. Snapshots of the time evolution of outer circuits as observed from the oscilloscope confirm the occurrence of ZLS experimentally. The quality of ZLS is numerically verified by correlation coefficient and similarity function measures. Further, the transition to ZLS is verified from the changes in the largest Lyapunov exponents and the correlation coefficient as a function of the coupling strength. IPS is experimentally confirmed using time series plots and also can be visualized using the concept of localized sets which are also corroborated by numerical simulations. In addition, we have calculated the correlation of probability of recurrence to quantify the phase coherence. We have also analytically derived a sufficient condition for the stability of ZLS using the Krasovskii-Lyapunov theory.

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arXiv2012

Transition to complete synchronization and global intermittent synchronization in an array of time-delay systems

We report the nature of transitions from nonsynchronous to complete synchronization (CS) state in arrays of time-delay systems, where the systems are coupled with instantaneous diffusive coupling. We demonstrate that the transition to CS occurs distinctly for different coupling configurations. In particular, for unidirectional coupling, locally (microscopically) synchronization transition occurs in a very narrow range of coupling strength but for a global one (macroscopically) it occurs sequentially in a broad range of coupling strength preceded by an intermittent synchronization. On the other hand, in the case of mutual coupling a very large value of coupling strength is required for local synchronization and, consequently, all the local subsystems synchronize immediately for the same value of the coupling strength and hence globally synchronization also occurs in a narrow range of the coupling strength. In the transition regime, we observe a new type of synchronization transition where long intervals of high quality synchronization which are interrupted at irregular times by intermittent chaotic bursts simultaneously in all the systems, which we designate as global intermittent synchronization (GIS). We also relate our synchronization transition results to the above specific types using unstable periodic orbit theory. The above studies are carried out in a well known piecewise linear time-delay system.

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arXiv2012

Global and Partial Phase Synchronizations in Arrays of Piecewise Linear Time-Delay Systems

In this paper, we report the identification of global and partial phase synchronizations in linear arrays of unidirectionally coupled piecewise linear time-delay systems with two different coupling configurations. In particular, in a linear array with open end boundary conditions, global phase synchronization (GPS) is achieved by a sequential synchronization as a function of the coupling strength (a second order transition). Further, the asynchronous ones in the array with respect to the main sequentially synchronized cluster organize themselves to form clusters before they achieve synchronization with the main cluster. On the other hand, in a linear array with closed end boundary conditions (ring topology), partial phase synchronization (PPS) is achieved by forming different groups of phase synchronized clusters above some threshold value of the coupling strength (a first order transition) where they continue to be in a stable PPS state. We confirm the occurrence of both global and partial phase synchronizations in two different piecewise linear time-delay systems using various numerical methods.

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