Traveling of extreme events in network of counter-rotating nonlinear oscillators

Varshney, Vaibhav; Kumarasamy, Suresh; Mishra, Ajay; Biswal, B.; Prasad, Awadhesh

doi:10.1063/5.0059750

Cited by 22 publications

(3 citation statements)

References 74 publications

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“…A detailed study of the synchronization of time-varying networks was also found in [15]. Te literature on synchronization is huge, and one may refer to [1,3,4,6,8,10,[16][17][18][19][20][21][22] and references therein. Recently, several studies have dealt with the synchronization of complex networks with higher-order interactions [23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 97%

Synchronizability of Discrete Nonlinear Systems: A Master Stability Function Approach

Ramasamy,

Kumarasamy,

Sampathkumar

et al. 2023

Complexity

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In recent times, studies on discrete nonlinear systems received much attention among researchers because of their potential applications in real-world problems. In this study, we conducted an in-depth exploration into the stability of synchronization within discrete nonlinear systems, specifically focusing on the Hindmarsh–Rose map, the Chialvo neuron model, and the Lorenz map. Our methodology revolved around the utilization of the master stability function approach. We systematically examined all conceivable coupling configurations for each model to ascertain the stability of synchronization manifolds. The outcomes underscored that only distinct coupling schemes manifest stable synchronization manifolds, while others do not exhibit this trait. Furthermore, a comprehensive analysis of the master stability function’s behavior was performed across a diverse range of coupling strengths σ and system parameters. These findings greatly enhance our understanding of network dynamics, as discrete-time dynamical systems adeptly replicate the dynamics of continuous-time models, offering significant reductions in computational complexity.

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Section: Introductionmentioning

confidence: 97%

Synchronizability of Discrete Nonlinear Systems: A Master Stability Function Approach

Ramasamy,

Kumarasamy,

Sampathkumar

et al. 2023

Complexity

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“…In the study of temporal dynamics of many dynamical systems, the occurrence of infrequent but recurrent comparatively high or low amplitude events might have qualitative similarities with occasional large events being recorded in many real-world phenomena. The emergence of EEs is reported in several dynamical systems such as FitzHugh-Nagumo oscillators, 29,[31][32][33][34][35] Hindmarsh-Rose model, 36 Liénard system, 37 Ikeda map, 25 Josephson junctions, 38 Ginzburg-Landau model, 39 nonlinear Schrödinger equation, 40 micromechanical system, 41 climatic models, 42 ecological model, 43 mechanical system, 44 and electronic circuits, 45 to name but a few. In addition, we also find some experimental evidence of the appearance of EEs, such as in laser systems, 46 epileptic EEG studies in rodents, 47 annular wave flume, 48 and laser systems, 49 to name but a few.…”

Section: Introductionmentioning

confidence: 99%

Extreme rotational events in a forced-damped nonlinear pendulum

Pal

Ray

Chowdhury³

et al. 2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Since Galileo’s time, the pendulum has evolved into one of the most exciting physical objects in mathematical modeling due to its vast range of applications for studying various oscillatory dynamics, including bifurcations and chaos, under various interests. This well-deserved focus aids in comprehending various oscillatory physical phenomena that can be reduced to the equations of the pendulum. The present article focuses on the rotational dynamics of the two-dimensional forced-damped pendulum under the influence of the ac and dc torque. Interestingly, we are able to detect a range of the pendulum’s length for which the angular velocity exhibits a few intermittent extreme rotational events that deviate significantly from a certain well-defined threshold. The statistics of the return intervals between these extreme rotational events are supported by our data to be spread exponentially at a specific pendulum’s length beyond which the external dc and ac torque are no longer sufficient for a full rotation around the pivot. The numerical results show a sudden increase in the size of the chaotic attractor due to interior crisis, which is the source of instability that is responsible for triggering large amplitude events in our system. We also notice the occurrence of phase slips with the appearance of extreme rotational events when the phase difference between the instantaneous phase of the system and the externally applied ac torque is observed.

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“…Thus, Lebedev et al demonstrated that rotations in neural population activity could represent spatiotemporal neural patterns best described as travelling waves [61]. Travelling waves are frequently encountered in neural datasets [62][63][64][65][66], including motor learning data [67], and reach-to-grasp movements [51,68], as well as datasets for RNNs trained for muscle activity production [69] and decision-making [41]. Additionally, Proix et al [70] demonstrated that a temporal covariance matrix structure creates a horseshoe artefact -a frequently encountered consequence of dimensionality reduction methods that yields rotations of state-space trajectories.…”

mentioning

confidence: 99%

On the Rotational Structure in Neural Data

Kuzmina,

Kriukov,

Lebedev

2023

Preprint

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Spatiotemporal properties of the activity of neuronal populations in cortical motor areas have been the subject of many experimental and theoretical investigations, which generated numerous interpretations regarding the mechanisms of preparing and executing limb movements. Two competing models, namely representational and dynamical models, strive to explain the temporal course of neuronal activity and its relationship with different paramaters of movements. One proposed dynamical model employs the jPCA method, a dimensionality reduction technique, to holistically characterize oscillatory activity in a population of neurons by maximizing rotational dynamics that are present in the data. Different interpretations have been proposed for the rotational dynamics revealed with jPCA approach in various brain areas. Yet, the nature of such dynamics remains poorly understood. Here we conducted a comprehensive analysis of several neuronal-population datasets. We demonstrated that rotational dynamics were consistently accounted for by a travelling wave pattern. To quantify the rotation strength, we developed a complex-valued measure termed the gyration number. Additionally, we identify the parameters influencing the extent of rotation in the data. Overall, our findings suggest that rotational dynamics and travelling waves are the same phenomena, which requires reevaluation of the previous interpretations where they were considered as separate entities.

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Traveling of extreme events in network of counter-rotating nonlinear oscillators

Cited by 22 publications

References 74 publications

Synchronizability of Discrete Nonlinear Systems: A Master Stability Function Approach

Synchronizability of Discrete Nonlinear Systems: A Master Stability Function Approach

Extreme rotational events in a forced-damped nonlinear pendulum

On the Rotational Structure in Neural Data

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