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We perform a detailed analysis of the sunspot number time series to reconstruct the phase space of the underlying dynamical system. The features of this phase space allow us to describe the behavior of the solar cycle in terms of a simple relaxation oscillator in two dimensions. The absence of systematic self-crossings suggests that the complexity of the sunspot time series does not arise as a consequence of chaos. Instead, we show that it can be adequately modeled through the introduction of adoi:10.1103/physrevlett.85.5476 pmid:11136025 fatcat:f4ls4mje2na7ngm3yqd3663sfa