Title :
Class 1 neural excitability, conventional synapses, weakly connected networks, and mathematical foundations of pulse-coupled models
Author :
Izhikevich, Eugene M.
Author_Institution :
Center for Syst. Sci. & Eng., Arizona State Univ., Tempe, AZ, USA
fDate :
5/1/1999 12:00:00 AM
Abstract :
Many scientists believe that all pulse-coupled neural networks are toy models that are far away from the biological reality. We show, however, that a huge class of biophysically detailed and biologically plausible neural-network models can be transformed into a canonical pulse-coupled form by a piece-wise continuous, possibly noninvertible, change of variables. Such transformations exist when a network satisfies a number of conditions; e,g., it is weakly connected; the neurons are Class 1 excitable (i.e., they can generate action potentials with an arbitrary small frequency); and the synapses between neurons are conventional (i.e., axo-dendritic and axe-somatic). Thus, the difference between studying the pulse-coupled model and Hodgkin-Huxley-type neural networks is just a matter of a coordinate change. Therefore, any piece of information about the pulse-coupled model is valuable since it tells something about all weakly connected networks of Class 1 neurons. For example, we show that the pulse-coupled network of identical neurons does not synchronize in-phase. This confirms Ermentrout´s (1996) result that weakly connected Class 1 neurons are difficult to synchronize, regardless of the equations that describe dynamics of each cell
Keywords :
bifurcation; dynamics; neural nets; neurophysiology; physiological models; Class 1 neural excitability; Hodgkin-Huxley-type neural networks; biologically plausible neural-network models; conventional synapses; pulse-coupled models; pulse-coupled network; pulse-coupled neural networks; weakly connected networks; Bifurcation; Biological neural networks; Biological system modeling; Equations; Frequency synchronization; Limit-cycles; Mathematical model; Neural networks; Neurons; Neurotransmitters;
Journal_Title :
Neural Networks, IEEE Transactions on