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Emerging Frontiers in Nonlinear Science pp 305–322Cite as

Synchronization in Discrete Models

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Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 32))

Abstract

In this chapter we discuss the emergence of a collective behavior in systems of discrete units with all to all interactions. Our focus is two fold: first we discuss the differences between systems with an infinite number of units (corresponding to a mean field approximation) and systems with finite populations; we also discuss conditions for systems with a finite number of states to be able to describe the continuous Kuramoto model.

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Acknowledgements

A.R. acknowledges the financial support of CPNq (Grant No.308344/2018-9). D.E. thanks funding from Fondecyt-Chile (Grant No.1170669).

Author information

Authors and Affiliations

  1. Departamento de Física, CCEN, Universidade Federal da Paraíba, Caixa Postal 5008, 58059-900, João Pessoa, Brazil

    Alexandre Rosas

  2. Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Av. Monseñor Alvaro del Portillo, 12455, Las Condes, Santiago, Chile

    Daniel Escaff

  3. Department of Chemistry and Biochemistry and BioCircuits Institute, University of California San Diego, La Jolla, CA, 92093-0340, USA

    Katja Lindenberg

Authors
  1. Alexandre Rosas
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  2. Daniel Escaff
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  3. Katja Lindenberg
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Corresponding author

Correspondence to Katja Lindenberg .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, USA

    Panayotis G. Kevrekidis

  2. Grupo de Fisica No Lineal, Departamento de Fisica Aplicada I, Escuela Politécnica Superior, Universidad de Sevilla, Seville, Spain

    Jesús Cuevas-Maraver

  3. Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA

    Avadh Saxena

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Rosas, A., Escaff, D., Lindenberg, K. (2020). Synchronization in Discrete Models. In: Kevrekidis, P., Cuevas-Maraver, J., Saxena, A. (eds) Emerging Frontiers in Nonlinear Science. Nonlinear Systems and Complexity, vol 32. Springer, Cham. https://doi.org/10.1007/978-3-030-44992-6_13

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