The complex dynamics of Alfvén waves described by the derivative nonlinear Schrödinger equation is investigated. In a region of the parameters space where multistability is observed, this complex system is driven towards an intermittent regime by the addition of noise. The effects of Gaussian and non-Gaussian noise are compared. In the intermittent regime, the Alfvén wave exhibits random qualitative changes in its dynamics as the result of a competition between three attractors and a chaotic saddle embedded in the fractal basin boundary.
[1] We present an overview of observational and theoretical evidence of chaos and intermittency in the solar-terrestrial environment including solar dynamo, solar atmosphere, solar wind, and terrestrial magnetosphere-ionosphere-atmosphere. The chaotic nature of space plasmas is studied by a nonlinear model of Alfvén waves described by the low-dimensional limit of the derivative nonlinear Schrödinger equation given by its stationary solutions in the frame moving with the driver wave velocity. A periodic window of the bifurcation diagram is constructed to identify two types of Alfvén chaos related to type-I intermittency and crisis-induced intermittency. We show that an Alfvén chaotic attractor is composed of chaotic saddles and unstable periodic orbits and explain the links between these unstable structures and Alfvén intermittency. The role of interplanetary Alfvén intermittency in the solar wind driving of intense geomagnetic activities is discussed.
Abstract. The chaotic dynamics of Alfvén waves in space plasmas governed by the derivative nonlinear Schrödinger equation, in the low-dimensional limit described by stationary spatial solutions, is studied. A bifurcation diagram is constructed, by varying the driver amplitude, to identify a number of nonlinear dynamical processes including saddlenode bifurcation, boundary crisis, and interior crisis. The roles played by unstable periodic orbits and chaotic saddles in these transitions are analyzed, and the conversion from a chaotic saddle to a chaotic attractor in these dynamical processes is demonstrated. In particular, the phenomenon of gap-filling in the chaotic transition from weak chaos to strong chaos via an interior crisis is investigated. A coupling unstable periodic orbit created by an explosion, within the gaps of the chaotic saddles embedded in a chaotic attractor following an interior crisis, is found numerically. The gapfilling unstable periodic orbits are responsible for coupling the banded chaotic saddle (BCS) to the surrounding chaotic saddle (SCS), leading to crisis-induced intermittency. The physical relevance of chaos for Alfvén intermittent turbulence observed in the solar wind is discussed.
The effects of noise in the dynamics of Alfvén waves described by the derivative nonlinear Schrödinger equation are investigated. In a complex region of the parameter space, where multistability is observed, an external stochastic source can effectively destroy attractors present in the noise-free system, as well as induce chaotic transients and extrinsic intermittency. In the intermittent regime, the Alfvén wave exhibits random qualitative changes in its behavior as a result of a competition between three attractors and a chaotic saddle embedded in the fractal basin boundary.
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