A closed system of three nonlinear coupled equations is presented, phenomenologically describing the source and loss mechanisms for waves and particles in the outer trapping regions. The principle variable parameters are total particle flux, diffusion rate, and wave growth rate. The equations combine elements suggested in earlier work to represent distinct aspescts of the coupled interactions. The equations include effects of particle drift and wave propagation transverse to the magnetic field lines. The behavior of the system is examined in the linearized approximation of small amplitude perturbations, to define the parameter space regions where oscillatory or growing solutions appear. It is shown that auroral electron precipitation pulsations at a frequency of ~0.1 Hz can occur in a limited region where oscillatory solutions are found that grow at a rate comparable with their frequecy. A stationary, nongrowing solution is found with a characteristic frequency of about 3 Hz which might appear as a modulation of the particle precipitation flux. Other growing solutions are found with characteristic periods so long that they are probably not important in the outer trapping regions which are disturbed by substorms at intervals of hours to days. Spatial scales are not set by the coupled equations but must be determined by external influences.