Synchronisation and Non-autonomicity

Thermodynamic openness is key to the long-term stability of living systems and can yield rich dynamical behaviours. Here, we model openness in coupled oscillator systems by introducing an external driving with time-varying parameters. Five systems of increasing complexity are considered: three cases of single driven oscillators followed by two cases of driven networks. We show how the time-varying parameters can enlarge the range of other parameters for which synchronous behaviour is stable. In addition, it can yield additional behaviours such as intermittent synchronisation. The stability of these systems is analysed via short- and long-time Lyapunov exponents, both analytically and numerically. The different dynamical regimes are also described via time-frequency representation. Finally, we compare the stabilising effect of deterministic non-autonomous driving to that of bounded noise. All in all, we give an overview of some effects time-varying parameters can have on synchronisation. These effects could be a key to understand how living systems maintain stability in the face of their ever-changing environment.