Abstract. A non-linear oscillator model of a simple system analogous to Earth-like magnetotail plasmoid formation and release dynamics is presented. In this context, Earth-like refers to any magnetosphere with an upstream bow-shock and an elongated downstream tail that undergoes tail plasmoid formation and release. It includes, for the first time in such a model, separate drivers for the Dungey and Vasyliunas Cycles and the capacity to include stochastic and deterministic driving in varying relative and absolute terms. The effects of measurement noise on the model output can also be simulated. This makes the model suitable to investigate the magnetotail dynamics of Mercury, Earth, Jupiter, Saturn and hypothetical exoplanets with similar magnetospheric configurations. The capacity to predict, in general terms, the behavior of a wide range of stellar-wind – magnetosphere interactions has become even more important in the light of the discovery of thousands of exoplanets in recent years. This model represents the first step towards being able to make such predictions for a wide variety of cases without resorting to detailed modelling of individual cases. It is demonstrated that the model can exhibit limit cycle (periodic) and chaotic (long-term unpredictable) behavior. The effects of a sufficiently strong dynamical noise component (stochastic driving) are shown to be inherently different from the effects of an equivalent level of simulated observational noise (simulated Gaussian instrument error). The possibilities of chaotic behavior and of dynamical noise dominating the underlying determinism imply that often only short-term forecasting of magnetotail plasmoid formation is possible.