LS2N, Université de Nantes
Date(s) : 17/06/2019 iCal
11 h 00 min - 12 h 00 min
Many systems in nature, especially living systems, can be modelled as a collection of interacting oscillators. Such systems can exhibit a plethora of behaviours, amongst which synchronisation, a state of maximal coherence, is of crucial importance. Indeed, the synchronisation of the beat of heart cells is as necessary as the synchronisation of neurons can be a bad pre-seizure sign. So far, ensembles of oscillators have been studied mostly as closed systems so that all parameters such as coupling or frequencies are constant. Very often, however, living systems are open and under the non-negligible influence of their environment, which is in general varying with time. This in turn influence internal parameters of the systems: the frequency of our heartbeat is far from constant, for example. Here, we include time-variability in our mode, and see the effect it has on the dynamics and its stability.
Here, we will see how time-variability can benefit or reduce stability in two scenarios: a temporal network (time-varying topology), and a network driven by an external oscillator with a time-varying frequency. We will discuss how, in the first case, synchronization is negatively affected, but that the region of synchronization is enlarged in the second case. Moreover, we will discuss the importance of looking into the dynamics of such systems at both short and long timescales. Time-varying features in models of living systems can bring us closer to realistic models, and allow us to reveal richer dynamics resulting from it.