Nonlinear Analysis in the Frequency Domain Neural Excitability Bursting Bifurcations in Neuron Dynamics Nonlinear Analysis in the Frequency Domain Synchronization and locking are ubiquitous in nature. Locking is prominent in the brain. We develop novel, nonlinear methods of analysis and modeling of neuronal activity. From mathematical point of view a system is excitable when small perturbations near a rest state can cause large excursions for the solution before it returns to the rest.
Systems are excitable because they are near bifurcations from rest to oscillatory dynamics.
The type of bifurcation determines excitable properties and hence neuro-computational features of the brain cells. Revealing these features is the most important goal of mathematical neuroscience. When neuron activity alternates between a quiescent state and repetitive spiking, the neuron activity is said to be bursting. Bifurcation of a spiking attractor that leads to quiescence. These bifurcations determine the type of burster and hence its neuro-computational features.