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Bifurcations and collective states of Kuramoto oscillators with higher-order interactions and rotational symmetry
Antonio Mihara1, Célia M Kuwana2, Roberto C Budzinski3,4,5
1Departamento de Física, Universidade Federal de São Paulo, UNIFESP Campus, Diadema, SP, Brazil.
Abstract:
We study a network of identical Kuramoto oscillators with higher-order interactions that also break the rotational symmetry of the system. To gain analytical insights into this model, we use the Watanabe-Strogatz Ansatz, which allows us to reduce the dimensionality of the original system of equations. The study of stability and bifurcations of the reduced system reveals a codimension two Bogdanov-Takens bifurcation and several other associated bifurcations. Such analysis is corroborated by numerical simulations of the associated Kuramoto system, which, in turn, unveils a variety of collective behaviors such as synchronized motion, oscillation death, chimeras, incoherent states, and traveling waves. Importantly, this system displays a case where alternating chimeras emerge in an indistinguishable single population of oscillators, which may offer insights into the unihemispheric slow-wave sleep phenomenon observed in mammals and birds.
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