IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v104y2017icp418-425.html
   My bibliography  Save this article

Synchronization and 1/f signals in interacting small-world networks

Author

Listed:
  • Aguilar-Velázquez, D.
  • Guzmán-Vargas, L.

Abstract

We investigated the synchronization and temporal correlations in a simple signaling network model. The model, which is able to display spatio-temporal avalanches and diverse fractal time correlations, consists of Boolean units located in a small-world network. We evaluated the synchrony between pairs of sets of units by means of the global lability synchronization measure, which is based on the probability of change of the total number of synchronized signals, for a range of evolutions of the system with different correlation dynamics. Here, we show that the global lability distribution exhibits power-law scaling for large-scale dynamics identified with 1/f signals, whereas a breakdown in the scaling behavior emerges when there are deviations toward either short-term correlated or uncorrelated dynamics. Furthermore, we extend our study to interacting multilayer networks, which consist of two small-world networks with different correlation dynamics in each layer. We evaluated the change in the correlation and the synchronization dynamics displayed by the system in terms of the coupling parameter between layers. Our results show that long-range correlated fluctuations naturally emerge or are still present even when coupled layers initially display different correlation dynamics. Moreover, the correlation-synchronization between pairs of global lability events closely follows a power-law scaling when networks are coupled, indicating that there exists a high correlation over long time scales due to information transmission.

Suggested Citation

  • Aguilar-Velázquez, D. & Guzmán-Vargas, L., 2017. "Synchronization and 1/f signals in interacting small-world networks," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 418-425.
    • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:418-425
    DOI: 10.1016/j.chaos.2017.08.034
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077917303636
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2017.08.034?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. D. Valenti & G. Augello & B. Spagnolo, 2008. "Dynamics of a FitzHugh-Nagumo system subjected to autocorrelated noise," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(3), pages 443-451, October.
    2. S. Spezia & L. Curcio & A. Fiasconaro & N. Pizzolato & D. Valenti & B. Spagnolo & P. Bue & E. Peri & S. Colazza, 2008. "Evidence of stochastic resonance in the mating behavior of Nezara viridula (L.)," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(3), pages 453-458, October.
    3. Manfred G Kitzbichler & Marie L Smith & Søren R Christensen & Ed Bullmore, 2009. "Broadband Criticality of Human Brain Network Synchronization," PLOS Computational Biology, Public Library of Science, vol. 5(3), pages 1-13, March.
    4. Joshua Milstein & Florian Mormann & Itzhak Fried & Christof Koch, 2009. "Neuronal Shot Noise and Brownian 1/f2 Behavior in the Local Field Potential," PLOS ONE, Public Library of Science, vol. 4(2), pages 1-5, February.
    5. B. Spagnolo & S. Spezia & L. Curcio & N. Pizzolato & A. Fiasconaro & D. Valenti & P. Lo Bue & E. Peri & S. Colazza, 2009. "Noise effects in two different biological systems," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 69(1), pages 133-146, May.
    6. Guzmán-Vargas, L. & Muñoz-Diosdado, A. & Angulo-Brown, F., 2005. "Influence of the loss of time-constants repertoire in pathologic heartbeat dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 304-316.
    7. Rudolf Hanel & Bernat Corominas-Murtra & Bo Liu & Stefan Thurner, 2017. "Fitting power-laws in empirical data with estimators that work for all exponents," PLOS ONE, Public Library of Science, vol. 12(2), pages 1-15, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ping, Zhu, 2023. "Analytical equivalent transformation method for nonlinear stochastic dynamics with multiple noises in high dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    2. Jin, Yanfei & Wang, Haotian & Xu, Pengfei, 2023. "Noise-induced enhancement of stability and resonance in a tri-stable system with time-delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    3. Guo, Yongfeng & Ding, Jiaxin & Mi, Lina, 2024. "Statistical complexity and stochastic resonance of an underdamped bistable periodic potential system excited by Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    4. Zhu, Ping, 2021. "An equivalent analytical method to deal with cross-correlated exponential type noises in the nonlinear dynamic system," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    5. Zueva Marina V, 2018. "A New Look at Stimulation Therapy with Complex-Structured Stimuli in Traumatic Brain Injuries," Global Journal of Addiction & Rehabilitation Medicine, Juniper Publishers Inc., vol. 5(1), pages 12-16, January.
    6. Federico Malizia & Santiago Lamata-Otín & Mattia Frasca & Vito Latora & Jesús Gómez-Gardeñes, 2025. "Hyperedge overlap drives explosive transitions in systems with higher-order interactions," Nature Communications, Nature, vol. 16(1), pages 1-10, December.
    7. Werner, Gerhard, 2013. "Consciousness viewed in the framework of brain phase space dynamics, criticality, and the Renormalization Group," Chaos, Solitons & Fractals, Elsevier, vol. 55(C), pages 3-12.
    8. Robert G. Sacco, 2019. "The Predictability of Synchronicity Experience: Results from a Survey of Jungian Analysts," International Journal of Psychological Studies, Canadian Center of Science and Education, vol. 11(3), pages 1-46, September.
    9. Christian Meisel & Alexander Storch & Susanne Hallmeyer-Elgner & Ed Bullmore & Thilo Gross, 2012. "Failure of Adaptive Self-Organized Criticality during Epileptic Seizure Attacks," PLOS Computational Biology, Public Library of Science, vol. 8(1), pages 1-8, January.
    10. Bashkirtseva, Irina & Ryashko, Lev, 2022. "Stochastic generation and shifts of phantom attractors in the 2D Rulkov model," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    11. Todd Zorick & Mark A Mandelkern, 2013. "Multifractal Detrended Fluctuation Analysis of Human EEG: Preliminary Investigation and Comparison with the Wavelet Transform Modulus Maxima Technique," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-7, July.
    12. Hernández-Pérez, R. & Angulo-Brown, F. & Tun, Dionisio, 2006. "Company size distribution for developing countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 359(C), pages 607-618.
    13. dos Santos, Maike A.F. & Junior, Luiz Menon, 2021. "Random diffusivity models for scaled Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    14. de la Cruz, H. & Jimenez, J. C, 2020. "Exact pathwise simulation of multi-dimensional Ornstein–Uhlenbeck processes," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    15. Ai, Hao & Yang, GuiJiang & Liu, Wei & Wang, Qiubao, 2023. "A fast search method for optimal parameters of stochastic resonance based on stochastic bifurcation and its application in fault diagnosis of rolling bearings," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    16. Fingelkurts, Andrew A. & Fingelkurts, Alexander A. & Neves, Carlos F.H., 2013. "Consciousness as a phenomenon in the operational architectonics of brain organization: Criticality and self-organization considerations," Chaos, Solitons & Fractals, Elsevier, vol. 55(C), pages 13-31.
    17. Bashkirtseva, Irina & Ryashko, Lev, 2023. "Transformations of spike and burst oscillations in the stochastic Rulkov model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    18. Guo, Shengli & Xu, Ying & Wang, Chunni & Jin, Wuyin & Hobiny, Aatef & Ma, Jun, 2017. "Collective response, synapse coupling and field coupling in neuronal network," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 120-127.
    19. Xu, Yong & Wu, Juan & Du, Lin & Yang, Hui, 2016. "Stochastic resonance in a genetic toggle model with harmonic excitation and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 91-100.
    20. Martinez-Saito, Mario, 2022. "Discrete scaling and criticality in a chain of adaptive excitable integrators," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:418-425. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.