Internal Reliability of Coupled Kuramoto-Sakaguchi Phase Oscillators

2026/06/24 by Arkady Pikovsky, Franco Bagnoli, Stefano Iubini · 1 voice
Physics and Astronomy · #nlin.CD

paper · pdf · doi:10.1088/2632-072x/ae8aa6

Abstract

The notion of internal reliability in dynamical networks describes whether replicas of a particular unit follow the dynamics of the reference unit. Reliability and anti-reliability can be quantified by the transversal Lyapunov exponents. We study phase oscillators coupled via Kuramoto-Sakaguchi-type interactions. Already the simplest solvable system of two oscillators demonstrates nontrivial reliability properties. We present numerical evidence of reliability and anti-reliability in small networks with a uniform distribution of natural frequencies. The dynamics of an ensemble of replicas can be described within the Watanabe-Strogatz theory, which predicts symmetry of the transversal Lyapunov exponents for replica-attractor and replica-repeller.

Citations

• Synchronization of branching chain of coupled maps: application to the logistic map
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• CHAOTIC ATTRACTOR IN THE KURAMOTO MODEL
• Synchronization and Maximum Lyapunov Exponents of Cellular Automata
• Are damage spreading transitions generically in the universality class of directed percolation?
• Constants of motion for superconducting Josephson arrays

Discussions

• Arkady Pikovsky, Franco Bagnoli, Stefano Iubini: Internal Reliability of Coupled Kuramoto-Sakaguchi Phase Oscillators https://arxiv.org/abs/2606.26172 https://arxiv.org/pdf/2606.26172 https://arxiv.or [bsky, 0 points, 0 comments]

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