2025/11/20 by A. V. Bobrova, Bobrova, A. V., G. V. Osipov +1
Computer Science · Physics and Astronomy · #Chaos control and synchronization #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Pattern Formation and Solitons (nlin.PS) #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2511.16307
openalex publication_date 2025/11/20 · openalex created_date 2025/11/23 · openalex updated_date 2026/07/28
This study investigates the collective dynamics (phase synchronization, instantaneous frequencies synchronization and mean frequencies synchronization) in an ensemble of four nonidentical phase oscillators with repulsive coupling. We use the Kuramoto-Sakaguchi system of ordinary differential equations as our mathematical model. Depending on the coupling strength in the presence of a small mismatch of the natural frequencies, all possible modes of frequency synchronization were found: 4:0 (global), 3:1, 2:2, 2:1:1 (cluster). It is shown that these regimes can be classified into two main types depending on the evolution of the instantaneous frequencies: stationary (4:0 and 2:2), characterized by constancy of phase ratios and instantaneous frequencies, and switching (3:1 and 2:1:1), in which metastable processes with periodic switching of synchronous states are observed: for different time intervals, different types of locking of instantaneous frequencies of oscillator pairs and different types of phase ratios were observed. For the 4:0 and 2:2 regimes, analytical expressions for the synchronization frequencies were derived. The presence of bistability has been revealed depending on the initial conditions of different synchronous regimes at the same parameters: sets of individual frequencies and value of coupling strength.