Transition of Magnetohydrodynamical Waves in the Solar Atmosphere
Transition to irregular behaviour of Magnetohydrodynamical (MHD) waves is investigated using a simple four-mode dynamical system worked out from the basic MHD equations by means of a Fourier and a multiple-scale analysis. In the initial stage of the transition, when most of the energy in concentrated in the low-wave-number Fourier component, the system behaves like a van dr Pol oscillator, exhibiting saddlenode bifurcations. Hopf bifurcations are found numerically when the low- and high-wavenumber components have comparable magnitude. Two Hopf bifurcations leading to a two-D torus are followed by bifurcation to a nonperiodic attractor.
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