arXiv subjects

S. Hariharan

Publications and source records attributed to S. Hariharan.

3 recordsLinked to original sources

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

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↗