arXiv subjects

Senthilvelan M

Publications and source records attributed to Senthilvelan M.

3 recordsLinked to original sources

arXiv2024

Intermittent cluster synchronization in a unidirectional ring of bursting neurons

We report a new mechanism through which extreme events with a dragon king-like distribution emerge in a network of unidirectional ring of Hindmarsh-Rose bursting neurons interacting through chemical synapses. We establish and substantiate the fact that depending on the choice of initial conditions, the neurons are divided into different clusters. These clusters transit from a phase-locked state (anti-phase) to phase synchronized regime with increasing value of the coupling strength. Before attaining phase synchronization, there exists some regions of the coupling strength where these clusters are phase synchronized intermittently. During such intermittent phase synchronization, extreme events originate in the mean-field of the membrane potential. This mechanism, which we name as intermittent cluster synchronization, is proposed as the new precursor for the generation of emergent extreme events in this system. These results are also true for diffusive coupling (gap junctions). The distribution of the local maxima of the collective observable shows a long tailed non-Gaussian while the interevent interval follows the Weibull distribution. The goodness of fit are corroborated using probability-probability plot and quantile-quantile plot. This intermittent phase synchronization becomes rarer and rarer with the increase in the number of clusters of initial conditions.

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arXiv2024

On examining the predictive capabilities of two variants of PINN in validating localised wave solutions in the generalized nonlinear Schrödinger equation

We introduce a novel neural network structure called Strongly Constrained Theory-Guided Neural Network (SCTgNN), to investigate the behaviours of the localized solutions of the generalized nonlinear Schrödinger (NLS) equation. This equation comprises four physically significant nonlinear evolution equations, namely, (i) NLS equation, Hirota equation Lakshmanan-Porsezian-Daniel (LPD) equation and fifth-order NLS equation. The generalized NLS equation demonstrates nonlinear effects up to quintic order, indicating rich and complex dynamics in various fields of physics. By combining concepts from the Physics-Informed Neural Network (PINN) and Theory-Guided Neural Network (TgNN) models, SCTgNN aims to enhance our understanding of complex phenomena, particularly within nonlinear systems that defy conventional patterns. To begin, we employ the TgNN method to predict the behaviours of localized waves, including solitons, rogue waves, and breathers, within the generalized NLS equation. We then use SCTgNN to predict the aforementioned localized solutions and calculate the mean square errors in both SCTgNN and TgNN in predicting these three localized solutions. Our findings reveal that both models excel in understanding complex behaviours and provide predictions across a wide variety of situations.

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arXiv2021

Symmetrical emergence of extreme events at multiple regions in a damped and driven velocity-dependent mechanical system

In this work, we report the emergence of extreme events in a damped and driven velocity-dependent mechanical system. We observe that the extreme events emerge at multiple points. We further notice that the extreme events occur symmetrically in both positive and negative values at all the points of emergence. We statistically confirm the emergence of extreme events by plotting the probability distribution function of peaks and interevent intervals. We also determine the mechanism behind the emergence of extreme events at all the points and classify these points into two categories depending on the region at which the extreme events emerge. Finally, we plot the two parameter diagram in order to have a complete overview of the system.

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