Modeling, Simulation, and Analysis for Hodgkin-Huxley Neuronal Network Dynamics
Mathematics, University of South Carolina
(April 23, 2013 3:00 PM - 3:50 PM)
The predictability of neuronal network dynamics is a central question in neuroscience. First, we present a numerical investigation of the network dynamics of coupled Hodgkin-Huxley (HH) neurons and show that there is a chaotic dynamical regime indicated by a positive largest Lyapunov exponent. In this regime, there is no numerical convergence of the solution and only statistical quantifications are reliable. Second, we introduce an efficient library-based numerical method for simulating HH neuronal networks. Our pre-computed high resolution data library can allow us to avoid resolving the spikes in detail and to evolve the HH neuron equations using much larger time steps than the typical ones used in standard methods. Meanwhile, we can achieve comparable resolution in statistical quantifications of the network activity. Finally, we present a coarse-grained event tree analysis for effectively discriminating small differences in inputs to the network dynamics.