Nonlinear Brain Dynamics via Neural Field Theory*

Going beyond well-known nonlinear effects at the single-neuron level , nonlinear effects at the systems and whole-brain levels are manifest in epileptic seizures (Hopf bifurcations, limit cycles, saddle cycles), migraines and visual hallucinations (Turing and Hopf-Turing patterns), strong visual stimulation (harmonic and subharmonic generation, phase locking, entrainment), deep brain stimulation therapy of Parkinson’s disease (entrainment, harmonic and subharmonic generation, resonance suppression), the natural 10 Hz alpha rhythm (bistability), and normal sleep-wake dynamics (near-criticality, hysteresis, critical slowing).

Recent analyses of the above nonlinear effects are surveyed here, showing that they can be explained by neural field theory, whose predictions reproduce experimental results on large-amplitude normal, abnormal, and driven brain oscillations.