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In this study, we first present a modeling mechanism for the loss of neurons in limbic brain regions (epileptogenic focus) that could cause epileptic seizures by spreading the pathological dynamics from the focal to healthy brain regions. Prior work has shown that Cellular Automata (CAs) are very effective in simulating physical systems and solving scientific problems by capturing essential global features of the systems resulting from the collective effect of simple system components that interact locally. Nontrivial CAs are obtained whenever the dependence on the values at each CA site is nonlinear. Consequently, in this study, we show that brain activity in a healthy and epileptic state can be simulated by CA long-range interactions. Results from analysis of CA simulation data, as well as real electroencephalographic (EEG) data clearly show the efficiency of the proposed CA algorithm for simulation of the transition to an epileptic state. The results are in agreement with ones from previous studies about the existence of high-dimensional stochastic behavior during the healthy state and low-dimensional chaotic behavior during the epileptic state. The correspondence of the CA simulation results with the ones from real EEG data analysis implies that the spatiotemporal chaotic dynamics of the epileptic brain are similar to observed nonequilibrium phase transition processes in spatially distributed complex systems.

In this study, we present evidence for the co-existence of a SOC-like mechanism, of intermittent turbulence and a hidden low dimensional chaotic process underlying the solar activity. In particular, the original signal reveals a high dimensional stochastic character and a critical state according to a SOC process, since there in no clear discrimination between the original signal and its surrogate data concerning geometrical and dynamical characteristics of the solar time series. Furthermore, using the flat coefficient F we found evidence for intermittent turbulence behaviour. This result was based on the non-Gaussian character and the presence of long-range correlated plasma vorticity. This is in agreement with the low dimensional chaotic selforganization that was revealed after the application of a high pass filter to the original solar flares signal and provides further evidence for self organization in solar activity dynamics. Finally, the above results indicate the existence of a phase transitionlike process in the solar corona dynamics, from high dimensional stochastic states to strong intermittent turbulence and low dimensional chaotic states, according to a general theory of critical dynamics applied to the driven and distributed solar corona system.

Several contributions of the Thrace group to magnetospheric, solar, and planetary physics over the last three decades are summarized from the perspective of a paradigm shift in nonlinear plasma physics. The work by Dennis Papadopoulos on plasma instabilities has been a source of inspiration for our magnetospheric studies including the introduction of the chaos hypothesis.In the last three decades the magnetospheric plasma has been widely explored as a natural laboratory of far-from-equilibrium plasma processes such as nonlinear instabilities and turbulence. One of the most important research goals is to understand the basic elements of the solar wind-magnetosphereionosphere interaction. Two areas of particular importance are magnetospheric energetic particle bursts and substorm development both of which have been pursued intensively since the 1970s and 1980s. Particle bursts (E≥300keV) were detected in the distant and near-Earth plasma sheet, in the magnetosheath, and upstream from the Earth's bow shock. Our research showed that their source lies within the plasma sheet [1][2][3][4]. Furthermore, inside the plasma sheet and in the vicinity of the neutral sheet during strong or weak substorms local magnetic reconnection signatures were observed simultaneously with strong bulk plasma flows and energetic particle acceleration as well as plasma structures consistent with closed magnetic field structures, (i.e., magnetic islands) [5,6]. In order to understand this magnetospheric phenomenology we have used the framework of nonlinear and non-equilibrium plasma theory and considered deterministic chaos as an appropriate paradigm of the observed dynamics. However, the hypothesis of magnetospheric chaos as well as our first results on the existence of a magnetospheric strange attractor obtained by time-series analysis were initially confronted with strong criticism [7]. The first mathematical model of magnetospheric chaos was developed by Baker et al. [8] and based on Shaw's leaky faucet model [9]. Klimas and coworkers [10] extended the dripping-faucet model by including magnetotail geometry and plasma processes. These results were further supported by a series of studies mostly based on chaotic analysis [11][12][13][14][15][16][17]. At the same time the concept of magnetospheric self-organized criticality (SOC) was introduced as an alternative to the low-dimensional magnetospheric chaos theoretically [18] and through data analysis [19][20][21].

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