We investigate single charged particle dynamics in the earth's magnetotail by examining a reversal with simple spatial dependence (the field lines are parabolic) but with general time dependence, which includes the associated induction electric field. The parabolic spatial dependence has, in static models, been shown by previous authors to imply that various regular and stochastic regimes of behavior exist, with particles remaining in a given regime for all time t. Here we show that, in general, time dependence yields transitions in behavior between the various regimes of regular and stochastic behavior. We identify three independent parametric coordinates which are functions of the field spatial and temporal scales, and the particle gyroscales, and time, which will indicate the regime of particle behavior at any given t. For specific time dependent field models these parametric coordinates can be inverted to directly give the timescales for transitions between one regime of behavior and another in terms of the field and particle spatial and temporal scales. These parametric coordinates have no direct analogue in static models. For a general thinning and folding sheet (representing the magnetotail magnetic field close to the center plane just before substorm onset) this characterization implies that stochastic dynamics may only occur over a finite time period and may not occur under certain circumstances. This may have implications for our understanding of the role played by single particle dynamics in the destabilization or reconfiguration of the magnetotail current sheet associated with substorms. ¿ American Geophysical Union 1994