On deterministic chaos,stationarity, periodicity and intermittency in coronal bursts and flares

Solar and stellar flares are highly structured in space and in time, as is indicated for example by their radio signatures: the narrowband spikes, type III, type II and IV, and pulsation events. Structured in time are also the not flare related type I events (noise storms). The nature of this observationally manifest fragmentation is still not clear. Either, it can be due to stochastic boundary or initial conditions of the respective processes, such as inhomogeneities in the coronal plasma. Or else, a deterministic non-linear process is able to cause complicated patterns of these kinds.We investigate the nature of the fragmentation in time. The properties of processes we enquire are stationarity, periodicity, intermittency, and, with dimension estimating methods, we try to discriminate between stochastic and low-dimensional deterministic processes. Since the measured time series are rather short, the dimension estimate methods have to be used with care: we have developed an extended dimension estimate procedure consisting of five steps. Among others, it comprises again the questions of stationarity and intermittency, but also the more technical problems of temporal correlations, judging scaling and convergence, and limited number of data points (statistical limits).We investigate 3 events of narrowband spikes, 13 type III groups, 10 type I storms, 3 type II bursts and 1 type IV event of solar origin, and 3 pulsation-like events of stellar origin. They have in common that all of them have stationary phases, periodicities are rather seldom, and intermittency is quite abundant. However, the burst types turn out to have different characteristics. None of the investigated time series reveals a low-dimensional behaviour. This implies that they originate from complex processes having dimensions (degrees of freedom) larger than about 4 to 6, which includes infinity,i. e. stochasticity. The lower limit of the degrees of freedom is inferred from numerical experiments with known chaotic systems, using time series of similar lengths, and it depends slightly on the burst types.