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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

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Synchronicity in Non-smooth Competitive Networks with Threshold Nonlinearities

Journal of Applied Nonlinear Dynamics 8(4) (2019) 533--547 | DOI:10.5890/JAND.2019.12.002

Ulises Chialva, Walter Reartes

Departamento de Matemática, Universidad Nacional del Sur, Av. Alem 1253, 8000 Bahía Blanca, Buenos Aires, Argentina

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The synchronization of nodes is a widely reported phenomenon in a large variety of networks. However, the mechanisms that produce such behavior can not always be studied analytically. In this paper, certain non-smooth competitive networks with linear thresholds are studied with formal and numerical tools. We show that the symmetries of the network architecture allow to display and explain the synchronicity between the nodes. Finally it is demonstrated that in this type of non-smooth networks the synchronicity constitutes a bifurcation phenomenon related to the stability of limit cycles.


The work is supported by the Universidad Nacional del Sur (Grant no. PGI 24/L096).


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