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In 1979 Hones made an analogy between the formation and release of plasmoids in Earth’s magnetotail and the dripping of a leaky tap. In 1984 Shaw demonstrated that the dynamics of leaky taps can be chaotic. In 1990 Baker and Klimas modified Shaw’s model of dripping dynamics and applied it to Earth’s magnetotail. This model also demonstrated chaotic behaviour and hinted that Hones’ analogy was more than merely a pedagogical tool for understanding the Dungey Cycle. A generalisation of the “leaky tap” approach to magnetotail dynamics is presented which separately includes the Dungey Cycle and the Vasyliunas Cycle, thus making the model applicable not just to Earth but to planetary magnetotails in general, by adjusting the contributions of each Cycle. Drag and linear damping terms are included in the model. The possibility of variable amounts of noise in the dynamics of each Cycle is also included in the model, in contrast to its predecessors, making it a useful tool for assessing whether the observed dynamics are dominated by deterministic or stochastic behaviour. Results show, in the absence of noise, a change from periodic to chaotic behaviour (illustrated by fractal iterated maps) as the loading rate is increased. The effects of varying the level of damping in the model are also shown. Finally, the impact of including dynamical noise is presented.