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Synchronization and chimera state in a mechanical system

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Abstract

Synchronization phenomenon appears in several natural systems being associated with physical, chemical and biological processes. In brief, synchronization may be understood as a harmonization of two or more system behaviors following some patterns. This paper deals with synchronization analysis of a mechanical pendulum-chart system composed by a hierarchical network of three pendula coupled to each other through their own chart that receives continuous supply of energy via a base excitation. Dynamical patterns are classified and investigated in order to understand the conditions to each one of them. Asynchronous behaviors are analyzed including the chimera state defined as a symmetry break of the behavior of identical oscillator network. Numerical simulations indicate that patterns do not have a direct relation with periodicity. An energetic approach is proposed in order to define a measure of synchronized states, providing new insights about the origin of chimera state and its relationship with natural frequencies.

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Acknowledgements

The authors would like to acknowledge the support of the Brazilian Research Agencies CNPq, CAPES and FAPERJ.

Funding

Funding was provides by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico and Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro.

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  1. Center for Nonlinear Mechanics, COPPE – Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, 21.941.972, P.O. Box 68.503, Rio de Janeiro, RJ, Brazil

    Phablo R. Carvalho & Marcelo A. Savi

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Correspondence to Marcelo A. Savi.

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Carvalho, P.R., Savi, M.A. Synchronization and chimera state in a mechanical system. Nonlinear Dyn 102, 907–925 (2020). https://doi.org/10.1007/s11071-019-05441-4

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