Exploring the interplay of excitatory and inhibitory interactions in the Kuramoto model on circle topologies

Albert Díaz-Guilera; Dimitri Marinelli; Conrad J. Pérez-Vicente

doi:10.1063/5.0204079

journal article Open Access Apr 01, 2024

Exploring the interplay of excitatory and inhibitory interactions in the Kuramoto model on circle topologies

Albert Díaz-Guilera

Dimitri Marinelli

Conrad J. Pérez-Vicente

Chaos: An Interdisciplinary Journal of Nonlinear Science Vol. 34 No. 4 · AIP Publishing

View at Publisher Save 10.1063/5.0204079

Abstract

In the field of collective dynamics, the Kuramoto model serves as a benchmark for the investigation of synchronization phenomena. While mean-field approaches and complex networks have been widely studied, the simple topology of a circle is still relatively unexplored, especially in the context of excitatory and inhibitory interactions. In this work, we focus on the dynamics of the Kuramoto model on a circle with positive and negative connections paying attention to the existence of new attractors different from the synchronized state. Using analytical and computational methods, we find that even for identical oscillators, the introduction of inhibitory interactions modifies the structure of the attractors of the system. Our results extend the current understanding of synchronization in simple topologies and open new avenues for the study of collective dynamics in physical systems.

Topics

No keywords indexed for this article. Browse by subject →

References

45

[1]

[2]

(1984)

[3]

"From Kuramoto to crawford: Exploring the onset of synchronization in populations of coupled oscillators" Phys. D: Nonlinear Phenom. (2000) 10.1016/s0167-2789(00)00094-4

[4]

(2001)

[5]

(2003)

[6]

"The Kuramoto model: A simple paradigm for synchronization phenomena" Rev. Mod. Phys. (2005) 10.1103/revmodphys.77.137

[7]

"The Kuramoto model in complex networks" Phys. Rep. (2016) 10.1016/j.physrep.2015.10.008

[8]

"The Kuramoto model revisited" J. Stat. Mech.: Theory Exp. 10.1088/1742-5468/aadb05

[9]

"Synchronization in complex networks" Phys. Rep. (2008) 10.1016/j.physrep.2008.09.002

[10]

"Synchronization in complex networks of phase oscillators: A survey" Autom. (2014) 10.1016/j.automatica.2014.04.012

[11]

"Complex networks: Structure and dynamics" Phys. Rep. (2006) 10.1016/j.physrep.2005.10.009

[12]

"Synchronization processes in complex networks" Phys. D: Nonlinear Phenom. (2006) 10.1016/j.physd.2006.09.029

[13]

"There is no non-zero stable fixed point for dense networks in the homogeneous Kuramoto model" J. Phys. A: Math. Theor. (2012) 10.1088/1751-8113/45/5/055102

[14]

[15]

"Synchronization of Kuramoto oscillators in dense networks" Nonlinearity (2020) 10.1088/1361-6544/ab9baa

[16]

"A global synchronization theorem for oscillators on a random graph" Chaos (2022) 10.1063/5.0090443

[17]

"Stability of phase locking in a ring of unidirectionally coupled oscillators" J. Phys. A: Math. Gen. (2004) 10.1088/0305-4470/37/46/004

[18]

"The size of the sync basin" Chaos (2006) 10.1063/1.2165594

[19]

"The size of the sync basin revisited" Chaos (2017) 10.1063/1.4986156

[20]

"How basin stability complements the linear-stability paradigm" Nat. Phys. (2013) 10.1038/nphys2516

[21]

"Basins with tentacles" Phys. Rev. Lett. (2021) 10.1103/physrevlett.127.194101

[22]

"Multistability of phase-locking and topological winding numbers in locally coupled Kuramoto models on single-loop networks" J. Math. Phys. (2016) 10.1063/1.4943296

[23]

"On the basin of attractors for the unidirectionally coupled Kuramoto model in a ring" SIAM J. Appl. Math. (2012) 10.1137/110829416

[24]

"Synchronization of coupled oscillators in a local one-dimensional Kuramoto model" Acta Phys. Pol. B, Proc. Suppl. (2010)

[25]

"Multistable behavior above synchronization in a locally coupled Kuramoto model" Phys. Rev. E (2011) 10.1103/physreve.83.066206

[26]

"Synchronization patterns in rings of time-delayed Kuramoto oscillators" Commun. Nonlinear Sci. Numer. Simul. (2021) 10.1016/j.cnsns.2020.105505

[27]

[28]

"The Kuramoto model on oriented and signed graphs" SIAM J. Appl. Dyn. Syst. (2019) 10.1137/18m1203055

[29]

"Multistability of phase-locking in equal-frequency Kuramoto models on planar graphs" J. Math. Phys. (2017) 10.1063/1.4978697

[30]

Cycle flows and multistability in oscillatory networks

Debsankha Manik, Marc Timme, Dirk Witthaut

Chaos: An Interdisciplinary Journal of Nonlinear S... 2017 10.1063/1.4994177

[31]

"Functional control of oscillator networks" Nat. Commun. (2022) 10.1038/s41467-022-31733-2

[32]

"Kuramoto model of coupled oscillators with positive and negative coupling parameters: An example of conformist and contrarian oscillators" Phys. Rev. Lett. (2011) 10.1103/physrevlett.106.054102

[33]

[34]

[35]

[36]

"DifferentialEquations.jl—A performant and feature-rich ecosystem for solving differential equations in Julia" J. Open Res. Softw. (2017) 10.5334/jors.151

[37]

"Networkdynamics.jl–Composing and simulating complex networks in Julia" Chaos (2021) 10.1063/5.0051387

[38]

[39]

"Basin sizes depend on stable eigenvalues in the Kuramoto model" Phys. Rev. E (2022) 10.1103/physreve.105.l052202

[40]

[41]

"The structure and dynamics of multilayer networks" Phys. Rep. (2014) 10.1016/j.physrep.2014.07.001

[42]

"The physics of higher-order interactions in complex systems" Nat. Phys. (2021) 10.1038/s41567-021-01371-4

[43]

"Synchronization in networks of mobile oscillators" Phys. Rev. E (2011) 10.1103/physreve.83.025101

[44]

"Uber die abgrenzung der eigenwerte einer matrix" Izv. Akad. Nauk. USSR Otd. Fiz.-Mat. Nauk (1931)

[45]

Metrics

7

Citations

45

References

Details

Published: Apr 01, 2024
Vol/Issue: 34(4)
License: View

Authors

A

Albert Díaz-Guilera

Departament de Física de la Matèria Condensada, Universitat de Barcelona 1 , 08028 Barcelona, Spain; Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona 2 , 08028 Barcelona, Spain

D

Dimitri Marinelli

Departament de Física de la Matèria Condensada, Universitat de Barcelona 1 , 08028 Barcelona, Spain; Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona 2 , 08028 Barcelona, Spain

C

Conrad J. Pérez-Vicente

Departament de Física de la Matèria Condensada, Universitat de Barcelona 1 , 08028 Barcelona, Spain; Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona 2 , 08028 Barcelona, Spain

Funding

Generalitat de Catalunya Award: 2021SGR00856

Cite This Article

Albert Díaz-Guilera, Dimitri Marinelli, Conrad J. Pérez-Vicente (2024). Exploring the interplay of excitatory and inhibitory interactions in the Kuramoto model on circle topologies. Chaos: An Interdisciplinary Journal of Nonlinear Science, 34(4). https://doi.org/10.1063/5.0204079

Exploring the interplay of excitatory and inhibitory interactions in the Kuramoto model on circle topologies

You May Also Like