Neural architectures that are operative in higher order cognition, including consciousness, memory, and motor planning, undergo complex changes in global organization during neurological disease. Increasingly, neurostimulation is therapeutically used for restoring these functions, although the mechanisms of restoration are largely unknown. Extant studies reveal, on the other hand, that non-linear and dynamical principles govern global brain organization, seen in operational features such as persistence, stability, flexibility and non-localization that are likely to be evoked by neurostimulation. These dynamical features are instantiated in neural oscillations, a key mechanism regulating brain function and communication. Due to stochastic influences, oscillator synchronization and desynchronization exhibit limit cycle attractor dynamics, which are characterized by persistent phase modulation rather than fixed point, stationary phase locking. Phase modulation governs information exchange by temporally gating transfer and guiding the trajectory of information distribution. Activation of attractor forces by modest input drive induces dynamic, phase difference detuning that results in phase preference shifts, whereas strong input drive induces low stability phase relations that promote oscillator dissociation and new pair formation. These dynamical features of oscillator behavior are likely to facilitate information transfer to neural networks during neurostimulation of higher order functions.