Chaotic dynamics of the solar cycle

Mathematics – Dynamical Systems

Scientific paper

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Chaos, Dynamical Systems, Fluid Dynamics, Helioseismology, Nonlinear Systems, Oscillators, Solar Activity, Solar Cycles, Stellar Models, Sunspots, Mathematical Models, Periodic Variations, Stellar Rotation

Scientific paper

In modeling the solar cycle, we proceed on the assumption that the processes driving the solar cycle are deterministic. In that case, a chaotic model is a good choice for a description of its complexity. In our modeling, we suppose that the solar activity variation is composed of two distinct, coupled processes: one a conventionally chaotic system, and the other a nonlinear oscillator. This idea comes directly from our analysis of the observations. Since the sun's rotation period is one month, we do not use the daily sunspot number, but work with its monthly average. This quantity shows both the cyclic variation on the eleven year time scale and additional strong fluctuations. If we smooth the data to remove periods less than a year to two, we see the solar cycle clearly exposed. When we subtract this smoothed sunspot number from the monthly average, we obtain the fluctuations in the sunspot number. We show a comparison between the monthly averaged number and the fluctuations for a few cycles. There is a clear correlation between the level of solar activity, as measured by the sunspot number, and the amplitude of the fluctuations in this number. We suggest that the fluctuations and the cyclic behavior correspond to two distinct but interacting processes.

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