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Synchronization in Time-Varying and Evolving Complex Networks

Author

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  • Gualberto Solís-Perales

    (Deptartamento de Electrónica, Centro Universitarios de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Av. Revolución No. 1500, Col. Olímpica, Guadalajara Jal. C.P. 44430, Mexico)

  • José Luis Zapata

    (Deptartamento de Electrónica, Centro Universitarios de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Av. Revolución No. 1500, Col. Olímpica, Guadalajara Jal. C.P. 44430, Mexico)

  • Guillermo Obregón-Pulido

    (Deptartamento de Electrónica, Centro Universitarios de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Av. Revolución No. 1500, Col. Olímpica, Guadalajara Jal. C.P. 44430, Mexico)

Abstract

In this contribution, we present the synchronization in dynamical complex networks with varying couplings. We identify two kinds of variations—(i) Non autonomous (Time-varying) couplings: where the coupling strength depends exclusively on time, (ii) Autonomous or Varying couplings (evolution) where the coupling strength depends on the behavior of the interconnected systems. The coupling strength in (i) is exogenous whereas in (ii) the coupling strength is endogenous and is defined by the states of the systems in the nodes. The exponential stability of the synchronization is ensured for the non autonomous couplings, due to the imposition of the coupling strength. Whereas, in the case of evolutionary couplings the exponential stability of the synchronization is not guaranteed for all time, due to the couplings are not controlled or imposed. We present an overview of these features in complex networks and illustrated by means of numerical examples.

Suggested Citation

  • Gualberto Solís-Perales & José Luis Zapata & Guillermo Obregón-Pulido, 2020. "Synchronization in Time-Varying and Evolving Complex Networks," Mathematics, MDPI, vol. 8(11), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1939-:d:439260
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    References listed on IDEAS

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    1. Duncan J. Watts & Steven H. Strogatz, 1998. "Collective dynamics of ‘small-world’ networks," Nature, Nature, vol. 393(6684), pages 440-442, June.
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