Entraining chimeras: The effect of driving with regular, irregular, and real-world phases

Chimera states in coupled oscillator networks are paradigmatic examples of partial synchronization in nonlinear systems, with direct relevance to real-world network dynamics, such as neuronal dynamics. Since real-world networks are not isolated, but embedded in larger interacting systems, chimeras have also been studied under the influence of other networks and external signals. In particular, most prior work has treated periodic forcing of chimeras in the thermodynamic limit. As a consequence, it remains unclear how chimera states respond to external driving in finite-size networks, where they can spontaneously collapse into full synchronization. It is also largely unknown how realistic noisy drivers, rather than periodic signals, affect driver-response synchronization. To address these open questions, we drive a finite-size oscillator network that exhibits a chimera state with constant-angular-frequency phases and with the same phases superimposed with noise. We find that, for a specific range of angular-frequency mismatch and driving strength, we can entrain chimeras without causing them to collapse into full synchronization. Adding noise, in turn, reduces entrainment and facilitates collapses. As a real-world application of the driven chimera state framework, we also drive chimeras with phases from focal and nonfocal electroencephalography (EEG) signals recorded during seizure-free periods in patients with epilepsy. We observe that focal signals yield higher entrainment power, within-network coherence, and collapse power than nonfocal signals when the driver EEG's dominant frequency is close to the chimera's mean angular frequency. Away from this regime, nonfocal signals yield higher values of all three measures. The observed differences not only characterize focal and nonfocal signals, but may also provide additional insight into the seizure-free brain dynamics of epilepsy patients. In conclusion, beyond quantifying how external driving signals, with or without noise, affect the dynamics of chimera states that can collapse into full synchronization, this work further bridges the study of chimera states and epilepsy research.