arXiv subjects

V. K. Chandrasekar

Publications and source records attributed to V. K. Chandrasekar.

At least 19 recordsLinked to original sources

arXiv2026

Effect of biharmonic coupling in frequency-weighted Kuramoto oscillators

We investigate the collective dynamics of globally coupled phase oscillators with frequency-weighted biharmonic coupling. Although frequency-weighted and biharmonic extensions of the Kuramoto model have each been studied independently, their combined effect has remained unexplored. By combining numerical branch continuation with analytical stability analysis, we construct the complete phase diagram in the two-parameter coupling plane. The competition between the first- and second-harmonic interactions gives rise to three distinct collective states: the incoherent state (IC), the antipodal multibranch state (APMS), and the symmetry-broken multibranch state (SBMS). These states are separated by three bistable regions and a narrow tristable region in which all three states coexist as stable attractors. The transitions from the incoherent state to both ordered states are discontinuous and hysteretic, reflecting the explosive synchronization induced by frequency weighting, while the transition between the APMS and SBMS is also abrupt. Analytically, we derive the linear instability thresholds of the incoherent state together with the existence and local stability conditions for the SBMS, and show that the theoretical predictions are in good agreement with extensive numerical simulations.

nlin.AO↗

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.

nlin.AO↗

arXiv2026

Symmetry-induced activity patterns of active-inactive clusters in complex networks

Synchrony patterns characterize network states in which nodes organize into clusters based on their synchronized dynamics. The synchronized clusters may further exhibit either active or inactive states. The simultaneous invariance of active and inactive clusters of synchronized nodes poses a dynamical constraint because fluctuations from active clusters must cancel out for a desired cluster to be inactive. By exploiting permutation symmetries in the network structure and choosing dynamics on top such that internal dynamics and coupling functions are odd functions in the phase space, we demonstrate that this combination of structure and dynamics exhibits stable invariant patterns composed of coexisting active and inactive clusters. The symmetries in a network generate active clusters that are in antisynchrony with each other, resulting in the cancellation of fluctuations for clusters connected with these antisynchronous clusters. We use full network symmetries to obtain synchronized clusters, while quotient network symmetries are used to find coexisting active-inactive states of clusters. We show that as the coupling between nodes changes, active clusters lose their activity at different coupling values, and the network transitions from one activity pattern to another. Numerical simulations are presented for networks of Van der Pol and Stuart-Landau oscillators. Finally, we extend the master stability framework to these patterns and provide stability conditions for their existence.

nlin.AO↗

arXiv2026

Dynamics-induced activity patterns of active-inactive clusters in complex networks

Synchrony patterns describe network states in which nodes of a coupled dynamical system are grouped into clusters based on synchronization between nodes. Beyond simple synchrony, synchronized clusters may also exhibit active or inactive states, and the collection of all such clusters constitutes an activity pattern. Although these patterns may arise naturally in networks with permutation symmetries, the requirement of symmetries imposes a restrictive and often unrealistic assumption, as many real-world networks lack such symmetries. In this work, we present synchrony patterns of coexisting active-inactive clusters that cannot be identified through symmetries. Considering dynamical systems in which intrinsic dynamics and coupling functions are odd functions in phase space, we identify all possible patterns a network can exhibit through symmetry breaking of identically synchronized clusters. The symmetry breaking of invariant clusters generates antisynchronized clusters, allowing active-inactive clusters to coexist. We show that while active clusters are external equitable partitions, inactive clusters can be purely dynamics-induced. Starting with a symmetry-broken state, we show that the existence of different invariant patterns is a function of coupling strength and intercluster weights. Finally, by combining synchronization manifolds with the Laplacian eigenvectors, we identify transversal perturbations for these patterns and present a stability analysis.

nlin.AO↗

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.

nlin.AO↗

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.

nlin.AO↗

arXiv2026

Self-oscillations induced by self-induced torque in magnetic double tunnel junction

Self-oscillations of the magnetization due to self-induced torque (SIT) in a magnetic double tunnel junction that consists of perpendicularly polarized, pinned and free layers is investigated along with the field-like torque (FLT). The associated Landau-Lifshitz-Gilbert-Slonczewski equation is numerically analysed to exhibit the oscillations of magnetization driven by the current. From the numerical analysis, we show that the SIT is essential to generate oscillations in the order of GHz and without it the magnetization reaches steady state after exhibiting switching. Without FLT, the frequency of the oscillations decreases with the current while the power of oscillations increases. In the presence of the negative strength of the FLT the power spectral density confirms that the frequency, power and the Q-factor increase with the current. Also the tunability range and the rate at which the frequency enhances increase with the magnitude of the FLT.

cond-mat.mes-hall↗

arXiv2025

Tunable Dynamics of a Dipolar Quantum Battery: Role of Spin-Spin Interactions and Coherence

This study explores the energy storage dynamics of a quantum battery (QB) modeled using a dipolar spin system with Dzyaloshinskii-Moriya (DM) interaction. We examine the performance of this system in terms of ergotropy, instantaneous power, capacity, and quantum coherence using a two-qubit model. By solving the system's time evolution under cyclic unitary processes, we analyze how external parameters such as temperature, magnetic field, and DM interaction influence the charging behavior and quantum resources of the battery. The findings demonstrate that quantum coherence and DM interaction significantly enhance the energy storage efficiency and power output of the quantum battery, offering promising strategies for designing high-performance quantum energy storage devices. Furthermore, we investigate the performance of quantum battery under the influence of a common dephasing environment, which limits the long-term work-extraction capability of dipolar quantum batteries.

quant-ph↗

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.

nlin.CD↗

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, Erdős-Rényi (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 Rössler 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.

nlin.CD↗

arXiv2025

Swarmalators with frequency-weighted interactions

We investigate the role of frequency-weighted interactions in a solvable model of one-dimensional (1D) swarmalators confined to a ring, where both spatial and phase couplings are scaled by the heterogeneous natural frequencies of individual agents. Our analysis identifies three distinct collective states: the asynchronous state , the phase-wave state , and the bistrip mixed state characterized by antipodal clusters that are internally split into frequency-dependent sub-strips. We further establish that the onset of abrupt transitions are driven by heterogeneous coupling. Using a self-consistency analysis, we precisely determine the conditions for dynamical transitions among the identified states, thereby extending the theoretical understanding of swarmalator dynamics under heterogeneous interaction rules, which are in good agreement with the numerical simulation results.

nlin.AO↗

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↗

arXiv2025

Frustration Induced Chimeras and Motion in Two Dimensional Swarmalators

Swarmalators are phase oscillators capable of simultaneous swarming and synchronization, making them potential candidates for replicating complex dynamical states. In this work, we explore the effects of a frustration parameter in the phase interaction functions of a two-dimensional swarmalator model inspired by the solvable Sakaguchi-swarmalators that move in a one-dimensional ring. The impact of the frustration parameter in these models has been a topic of great interest. Real-world coupled systems with frustration exhibit remarkable collective dynamical states, underscoring the relevance of this study. The frustration parameter induces various states exhibiting non-stationarity, chimeric clustering, and global translational motion, where swarmalators move spontaneously in two-dimensional space. We investigate the characteristics of these states and their responses to changes in the frustration parameter. Notably, the emergence of chimeric states suggests the crucial role of non-stationarity in phase interactions for spontaneous population clustering. Additionally, we examine how phase non-stationarity influences the spatial positions of swarmalators and provide a classification of these states based on different order parameters.

nlin.AO↗

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.

nlin.CD↗

arXiv2024

Streamlined approach to mitigation of cascading failure in complex networks

Cascading failures represent a fundamental threat to the integrity of complex systems, often precipitating a comprehensive collapse across diverse infrastructures and financial networks. This research articulates a robust and pragmatic approach designed to attenuate the risk of such failures within complex networks, emphasizing the pivotal role of local network topology. The core of our strategy is an innovative algorithm that systematically identifies a subset of critical nodes within the network, a subset whose relative size is substantial in the context of the network's entirety. Enhancing this algorithm, we employ a graph coloring heuristic to precisely isolate nodes of paramount importance, thereby minimizing the subset size while maximizing strategic value. Securing these nodes significantly bolsters network resilience against cascading failures. The method proposed to identify critical nodes and experimental results show that the proposed technique outperforms other typical techniques in identifying critical nodes. We substantiate the superiority of our approach through comparative analyses with existing mitigation strategies and evaluate its performance across various network configurations and failure scenarios. Empirical validation is provided via the application of our method to real-world networks, confirming its potential as a strategic tool in enhancing network robustness.

nlin.AO↗

arXiv2024

Painlevé Analysis, Prelle-Singer Approach, Symmetries and Integrability of Damped Hénon-Heiles System

We consider a modified damped version of Hénon-Heiles system and investigate its integrability. By extending the Painlevé analysis of ordinary differential equations we find that the modified Hénon-Heiles system possesses the Painlevé property for three distinct parametric restrictions. For each of the identified cases, we construct two independent integrals of motion using the well known Prelle-Singer method. We then derive a set of nontrivial non-point symmetries for each of the identified integrable cases of the modified Hénon-Heiles system. We infer that the modified Hénon-Heiles system is integrable for three distinct parametric restrictions. Exact solutions are given explicitly for two integrable cases.

nlin.SI↗

arXiv2024

Disparity Driven Heterogeneous Nucleation in Finite-Size Adaptive Networks

Phase transitions are crucial in shaping the collective dynamics of a broad spectrum of natural systems across disciplines. Here, we report two distinct heterogeneous nucleation facilitating single-step and multi-step phase transitions to global synchronization in a finite-size adaptive network due to the trade-off between time scale adaptation and coupling strength disparities. Specifically, small intracluster nucleations coalesce either at the population interface or within the populations resulting in the two distinct phase transitions depending on the degree of the disparities. We find that the coupling strength disparity largely controls the nature of phase transition in the phase diagram irrespective of the adaptation disparity. We provide a mesoscopic description for the cluster dynamics using the collective coordinates approach that brilliantly captures the multicluster dynamics among the populations leading to distinct phase transitions. Further, we also deduce the upper bound for the coupling strength for the existence of two intraclusters explicitly in terms of adaptation and coupling strength disparities. These insights may have implications across domains ranging from neurological disorders to segregation dynamics in social networks.

nlin.AO↗

arXiv2023

Exploration of field-like torque and field-angle tunability in coupled spin-torque nano oscillators for synchronization

We investigate the influence of field-like torque and the direction of the external magnetic field on a one-dimensional array of serially connected spin-torque nano oscillators, having free layers with perpendicular anisotropy, to achieve complete synchronization between them by analyzing the associated Landau-Lifshitz-Gilbert-Slonczewski equation. The obtained results for synchronization are discussed for the cases of 2, 10 and 100 oscillators separately. The roles of the field-like torque and the direction of the external field on the synchronization of the STNOs are explored through the Kuramoto order parameter. While the field-like torque alone is sufficient to bring out global synchronization in the system made up of a small number of STNOs, the direction of the external field is also needed to be slightly tuned to synchronize the one-dimensional array of a large number of STNOs. The formation of complete synchronization through the construction of clusters within the system is identified for the 100 oscillators. The large amplitude synchronized oscillations are obtained for small to large numbers of oscillators. Moreover, the tunability in frequency for a wide range of currents is shown for the synchronized oscillations up to 100 spin-torque oscillators. In addition to achieving synchronization, the field-like torque increases the frequency of the synchronized oscillations. The transverse Lyapunov exponents are deduced to confirm the stable synchronization in coupled STNOs due to the field-like torque and to validate the results obtained in the numerical simulations. The output power of the array is estimated to be enhanced substantially due to complete synchronization by the combined effect of field-like torque and tunability of the field angle.

cond-mat.mes-hall↗