Chaos and multifractals in the solar wind

Wiesław M. Macek
2010 Advances in Space Research  
The nature of the fluctuations in solar wind plasma parameters is still very little understood. The slow solar wind most likely originates from nonlinear processes in the solar corona. However, it appears that a certain kind of order does lie concealed within the irregular solar wind fluctuations, which can be described using methods of nonlinear time series analysis, based on fractal analysis and the theory of deterministic chaos. This involves the notions of fractal and multifractal sets,
more » ... h could be presumably strange attractors in a certain state space of a given complex dynamical system. By employing the so-called false-nearest-neighbors method, we argue that the deterministic component of solar wind plasma dynamics should be low-dimensional. In fact, the results we have obtained using the method of topological embeddings indicate that the behavior of the solar wind can be approximately described by a low-dimensional chaotic attractor in the inertial manifold, which is a subspace of system phase space. We have also shown that the multifractal spectrum of the solar wind attractor is consistent with that for the multifractal measure of the self-similar generalized weighted Cantor set with two different scaling parameters describing nonuniform compression and one probability measure parameter of the chaotic attractor 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. WSEF, 20-25 October 2007, Alexandria, Egypt 1 We hope that this generalized multifractal model will be a useful tool for analysis of intermittent turbulence in space plasmas. We thus believe that fractal analysis of chaotic systems could lead us to a deeper understanding of their nature, and maybe even to predict their seemingly unpredictable behavior. WSEF, 20-25 October 2007, Alexandria, Egypt 2 Within the complex dynamics of the solar wind's fluctuating intermittent plasma parameters, there is a detectable, hidden order described by a strange chaotic attractor that exhibits a multifractal structure.
doi:10.1016/j.asr.2008.12.026 fatcat:bba2n3wubjckbabm7nqjdwoe6e