A set of nonlinear continuum field equations is presented which describes the dynamics of neural activity in cortex. These take into account the most pertinent anatomical and physiological features found in cortex with all parameter values obtainable from independent experiment. Derivation of a white noise fluctuation spectrum from a linearized set of equations shows the presence of strong resonances that correspond to electroencephalographically observed 0.3-4 Hz (mammalian delta), 4-8 Hz (mammalian theta), 8-13 Hz (mammalian alpha) and >13 Hz (mammalian beta) activity. Numerical solutions of a full set of one-dimensional nonlinear equations include properties analogous to cortical evoked potentials, travelling waves at experimentally observed velocities, threshold type spike activity and limit cycle, chaotic and noise driven oscillations at the frequency of the mammalian alpha rhythm. All these types of behaviour are generated with parameters that are within ranges reported experimentally. The strong dependence of the phenomena observed on inhibitory-inhibitory interactions is demonstrated. These results suggest that the classically described alpha may be instantiated in a number of qualitatively distinct dynamical regimes, all of which depend on the integrity of inhibitory-inhibitory population interactions.