Between phase and amplitude oscillators

Pau Clusella, Antonio Politi

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13 Citations (Scopus)
23 Downloads (Pure)


We analyze an intermediate collective regime where amplitude oscillators distribute themselves along a closed, smooth, time-dependent curve C, thereby maintaining the typical ordering of (identical) phase oscillators. This is achieved by developing a general formalism based on two partial differential equations, which describe the evolution of the probability density along C and of the shape of C itself. The formalism is specifically developed for Stuart-Landau oscillators, but it is general enough to apply to other classes of amplitude oscillators. The main achievements consist in (i) identification and characterization of a transition to self-consistent partial synchrony (SCPS), which confirms the crucial role played by higher Fourier harmonics in the coupling function; (ii) an analytical treatment of SCPS, including a detailed stability analysis; and (iii) the discovery of a different form of collective chaos, which can be seen as a generalization of SCPS and characterized by a multifractal probability density. Finally, we are able to describe given dynamical regimes at both the macroscopic and the microscopic level, thereby shedding additional light on the relationship between the two different levels of description.
Original languageEnglish
Article number062201
Number of pages15
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number6
Early online date3 Jun 2019
Publication statusPublished - Jun 2019

Bibliographical note

This work has been financially supported by the EU project COSMOS (642563). We wish to acknowledge Ernest Mont-brio for early suggestions and enlightening discussions.


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