Brain Dynamics:


Nancy Kopell

Nancy Kopell and colleagues study the collective rhythms that often emerge when many Hodgkin-Huxley type models are connected into a network. These rhythms, typically associated with synchronized spikes, are critical for functions as diverse as movement and attention.

Further Reading

N. Kopell, "We got rhythm: Dynamical systems of the nervous system,'' published version of the 1998 Gibbs Lecture of the AMS, Notices of the AMS, 47: 6-16 (2000)


Jonathan Rubin David Terman

Jonathan Rubin

David Terman

Jonathan Rubin, David Terman, and colleagues use networks of coupled Hodgkin and Huxley-type equations to simulate pathological rhythms that emerge in Parkinson Disease -- and how the Deep Brain Stimulation therapy can bring about its astounding clinical effects.

Further Reading

Jonathan Rubin and David Terman, "High frequency stimulation of the subthalamic nucleus eliminates pathological rhythmicity in a computational model," J. Comp. Neurosci., 16: 211-235, 2004.


John Rinzel Bard Ermentrout

John Rinzel

Bard Ermentrout

How can we tell one neuron model from another? Will we need a new analysis for each new model? John Rinzel and Bard Ermentrout have tackled these questions with dynamical systems tools. These methods connect together broad classes of Hodgkin-Huxley type models, based on their mathematical structure and spike-firing properties. They are joined in this challenging endeavor by many in the applied mathematics community!

Further Reading

Rinzel-J; Ermentrout-B, Analysis of neural excitability and oscillations, In "Methods in Neuronal Modelling: From synapses to Networks,'' C. Koch and I. Segev, eds. 1989, MIT Press (revised 1998).


David Chopp, Nelson Spruston, and Bill Kath, and colleagues zoom in on a finer scale, studying Hodgkin and Huxley-type equations within the wonderfully complex branched structures of dendrites. Questions of how neuron geometry and dynamics interact are paramount, and this team brings together modern computational methods and the latest experimental techniques to find answers.

Further Reading

T. Jarsky, A. Roxin, W. L. Kath and N. Spruston, "Conditional dendritic spike propagation following distal synaptic activation of hippocampal CA1 pyramidal neurons, Nature Neuroscience 8 (2005), pp. 1667-1676.

Michael J. Rempe, Nelson Spruston, William L. Kath and David L. Chopp, Compartmental neural simulations with spatial adaptivity, J. Computational Neuroscience, Springer (2008).


Brain visualizations courtesy of Chris Johnson and Nathan Galli, Scientific Computing and Imaging Institute, University of Utah