Neurons as dynamical systems and regimes of neuronal activity
Course duration: 6 h
Bifurcation theory is the study of transitions between or among regimes in dynamical systems in response to a controlling parameter. These transitions, or bifurcations, determine temporal characteristics and other properties of the recorded activity. The relation between membrane current and membrane potential in neurons is characteristically nonlinear. In neuroscience, contemporary bifurcation theory has been applied to the analysis of mechanisms underlying spiking, bursting, and chaotic regimes of activity of neuronal systems.
Bifurcation analysis in neuronal models is a powerful tool. Biophysical parameters are used as controlling parameters, and changes in regimes of activity can be identified concomitantly with bifurcations. The association of transitions between regimes of neuronal activity with specific bifurcations gives predictions about the properties of stationary and oscillatory solutions and describes mechanisms underlying these regimes. Bifurcation theory provides quantitative laws that govern activity for parameter values close to bifurcation. As such, the identification of specific dynamical mechanisms in neuronal models provides predictions about the response of a living neuron to changes in biophysical parameters or external perturbations. During the course students will be introduced to Matlab and bifurcation analysis program Content. Neuronal models will be build and analyzed, as well as the roles of different bifurcations in the control of different regimes of neuronal activity will be assessed.
Dr. Gennady S. Cymbalyuk
Place of employment: Dynamical Neuroscience Lab., The Neuroscience Institute, Georgia State University, Georgia, USA
Spheres of scientific research: Neurophysics, Central Pattern Generators, genesis and regulation of bursting activity, control of rhythmic movements, neuromodulation, multistability in neuronal dynamics, leech heart beat, hybrid systems composed of living neurons and mathematical model integrated in real-time, dynamic clamp.