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Network Synchronization of Piecewise-Linear Oscillators with Mean-Field Commutation Function.

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Title: Network Synchronization of Piecewise-Linear Oscillators with Mean-Field Commutation Function.
Authors: Pena Ramirez, J.1 (AUTHOR) jpena@cicese.edu.mx, Echenausía-Monroy, J. L.1 (AUTHOR) echenausia@cicese.edu.mx, Cuesta-García, J. R.1 (AUTHOR) jcuesta@cicese.edu.mx
Source: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering. Feb2026, Vol. 36 Issue 2, p1-18. 18p.
Subjects: Synchronization, Mean field theory, Hysteresis, Computer simulation, Stability theory, Harmonic oscillators
Abstract: In this work, we investigate the onset of synchronization in a network of Piecewise-Linear (PWL) oscillators. Instead of using a commutation function for each system, as usually assumed in the literature, here, we consider a common mean-field commutation function, which governs the oscillatory behavior of the whole network, where the oscillators are synchronized via diffusive coupling. Some of the advantages of the proposed approach are: a more tractable mathematical analysis of the stability of the synchronous solution and a reduction in the computational burden. We illustrate this by three examples: a network of planar systems driven by hysteresis, a network of multiscroll oscillators, and a network of PWL Rössler systems. In all cases, we provide analytic conditions that guarantee the asymptotic stability of the synchronous solution for different input–output combinations and also, we illustrate our findings by numerical simulations. Additionally, the effect of initial conditions on the boundedness of solutions in the network is numerically investigated. An interesting characteristic of the proposed mean-field commutation function approach is that the nodes in the network act as oscillators only if the whole network is synchronized; otherwise, the nodes behave as unstable systems. Thus, the proposed scheme rewards the cooperative motion but penalizes the divergent individual behavior. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Bifurcation & Chaos in Applied Sciences & Engineering is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 190698715
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PubTypeId: academicJournal
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  Data: Network Synchronization of Piecewise-Linear Oscillators with Mean-Field Commutation Function.
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  Data: <searchLink fieldCode="AR" term="%22Pena+Ramirez%2C+J%2E%22">Pena Ramirez, J.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jpena@cicese.edu.mx</i><br /><searchLink fieldCode="AR" term="%22Echenausía-Monroy%2C+J%2E L%2E%22">Echenausía-Monroy, J. L.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> echenausia@cicese.edu.mx</i><br /><searchLink fieldCode="AR" term="%22Cuesta-García%2C+J%2E R%2E%22">Cuesta-García, J. R.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jcuesta@cicese.edu.mx</i>
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  Data: <searchLink fieldCode="DE" term="%22Synchronization%22">Synchronization</searchLink><br /><searchLink fieldCode="DE" term="%22Mean+field+theory%22">Mean field theory</searchLink><br /><searchLink fieldCode="DE" term="%22Hysteresis%22">Hysteresis</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+theory%22">Stability theory</searchLink><br /><searchLink fieldCode="DE" term="%22Harmonic+oscillators%22">Harmonic oscillators</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: In this work, we investigate the onset of synchronization in a network of Piecewise-Linear (PWL) oscillators. Instead of using a commutation function for each system, as usually assumed in the literature, here, we consider a common mean-field commutation function, which governs the oscillatory behavior of the whole network, where the oscillators are synchronized via diffusive coupling. Some of the advantages of the proposed approach are: a more tractable mathematical analysis of the stability of the synchronous solution and a reduction in the computational burden. We illustrate this by three examples: a network of planar systems driven by hysteresis, a network of multiscroll oscillators, and a network of PWL Rössler systems. In all cases, we provide analytic conditions that guarantee the asymptotic stability of the synchronous solution for different input–output combinations and also, we illustrate our findings by numerical simulations. Additionally, the effect of initial conditions on the boundedness of solutions in the network is numerically investigated. An interesting characteristic of the proposed mean-field commutation function approach is that the nodes in the network act as oscillators only if the whole network is synchronized; otherwise, the nodes behave as unstable systems. Thus, the proposed scheme rewards the cooperative motion but penalizes the divergent individual behavior. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Bifurcation & Chaos in Applied Sciences & Engineering is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1142/S0218127426500173
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        Text: English
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        PageCount: 18
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      – SubjectFull: Synchronization
        Type: general
      – SubjectFull: Mean field theory
        Type: general
      – SubjectFull: Hysteresis
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      – SubjectFull: Computer simulation
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      – SubjectFull: Stability theory
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      – SubjectFull: Harmonic oscillators
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      – TitleFull: Network Synchronization of Piecewise-Linear Oscillators with Mean-Field Commutation Function.
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              Text: Feb2026
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              Y: 2026
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