Chaos and Multifractals in the Solar System Plasma

We argue that dynamical behavior of space plasmas can often be approximately described by low-dimensional chaotic attractors in the inertial manifold, which is a subspace of a given system phase space. In fact, using nonlinear time-series analysis based on the method of topological embedding, we have identified a chaotic strange attractor in the solar wind data. In particular, we have shown that the multifractal spectrum of the solar wind attractor is consistent with that for the self-similar generalized weighted Cantor set with one probability measure parameter of the chaotic attractor and one or possibly two scaling parameters describing nonuniform compression in the phase space of the system. The values of the parameters fitted demonstrate small dissipation of the complex solar wind plasma and show that some parts of the attractor in phase space are visited much more frequently than other parts.

To quantify the multifractality of space plasma turbulence, we have recently considered the generalized two-scale weighted Cantor set also in the context of solar wind intermittent turbulence. We investigate the resulting multifractal spectrum of generalized dimensions depending on parameters of the new cascade model, especially for asymmetric scaling. In particular, we show that intermittent pulses are stronger for the model with two different scaling parameters; a much better agreement with the solar wind data is obtained, especially for the negative index of the generalized dimensions.

Therefore we argue that there is a need to use a two-scale cascade model. We hope that this generalized multifractal model will be a useful tool for analysis of intermittent turbulence in the Solar System plasma. We thus believe that fractal analysis of chaotic phenomena in the complex space environment could lead us to a deeper understanding of their nature, and maybe even to predict their seemingly unpredictable behavior.