Work

Nonlinear bias of collective oscillation frequency induced by asymmetric Cauchy noise

Year: 2025

Type: article

Abstract: We report the effect of nonlinear bias of the frequency of collective oscillations of sin-coupled phase oscillators subject to individual asymmetric Cauchy noises. The noise asymmetry makes the Ott-Antonsen ansatz inapplicable. We argue that, for all stable non-Gaussian noises, the tail asymmetry is not only possible (in addition to the trivial shift of the distribution median) but also generic in many physical and biophysical setups. For the theoretical description of the effect, we develop a mathematical formalism based on the circular cumulants. The derivation of rigorous asymptotic results can be performed on this basis but seems infeasible in traditional terms of the circular moments (the Kuramoto-Daido order parameters). The effect of the entrainment of individual oscillator frequencies by the global oscillations is also reported in detail. The accuracy of theoretical results based on the low-dimensional circular cumulant reductions is validated with the high-accuracy "exact" solutions calculated with the continued fraction method.

Source: Chaos An Interdisciplinary Journal of Nonlinear Science

DOI: 10.1063/5.0239363

Authors: Maria V. Ageeva, Denis S. Goldobin

Institutions: Institute of Continuous Media Mechanics, Perm State University

Language: English

Topic: Nonlinear Dynamics and Pattern Formation

Subfield: Computer Networks and Communications

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Ministry of Science and Higher Education of the Russian Federation

Award: G3436679421