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Dissipative discrete breathers in a chain of Rayleigh oscillators

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Abstract

The dynamics of chains of interacting active particles with Rayleigh-type dissipation and coupled by a Morse potential were previously studied. In this work we introduce an on-site potential to transform this system into a chain of oscillators. We study the evolution of modes previously found in a chain of active particles as a consequence of the on-site force. Beside this, a new class of modes, dissipative discrete breathers, is found. These new modes appear due to the new time scales introduced by the on-site potential. Interaction of the dissipative discrete breathers is also investigated. We find different behaviors; for short chains dissipative discrete breathers can meet during the transitory formation reaching the stationary modes including the optical one, sufficiently long chains the dissipative discrete breathers reach its stationary state without interactions and for medium lengths, the dissipative discrete breathers interact by forming a standing wave in between.

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Acknowledgements

KSS and APC are grateful to the Russian Science Foundation for the support under Grant No. 1611-10163. EdelR is grateful to the Spanish Ministerio de Ciencia, Innovación y Universidades for the support under Grant No. RTI2018-094409-B-I00.

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Authors and Affiliations

  1. Saratov National Research State University, 83 Astrakhanskaya Street, Saratov, Russia, 410012

    K. S. Sergeev & A. P. Chetverikov

  2. Institute of Mathematical Problems of Biology-Branch of Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Professor Vitkevich St., 1, Pushchino, Moscow Region, Russia, 142290

    K. S. Sergeev & A. P. Chetverikov

  3. ETSI Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros, 3, 28040, Madrid, Spain

    E. del Rio

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  1. K. S. Sergeev
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Sergeev, K.S., Chetverikov, A.P. & del Rio, E. Dissipative discrete breathers in a chain of Rayleigh oscillators. Nonlinear Dyn 102, 1813–1823 (2020). https://doi.org/10.1007/s11071-020-06031-5

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