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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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Abstract

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.

Acknowledgments

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

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