Abstract
Synchronization in neural networks is believed to be linked to cognitive processes, while abnormal synchronization has been associated with disorders such as epilepsy and schizophrenia. We examine the synchronization of small Hodgkin–Huxley neuronal networks. The principal features of Hodgkin–Huxley neurons are protein channels in the neural membrane that transition between open and closed states with voltage dependent rate constants. The standard assumption of infinitely many channels neglects the fact that real neurons have finitely many channels, which leads to fluctuations in the membrane voltage and modifies neuronal spike times. These fluctuations are referred to as channel noise. We demonstrate that regardless of channel noise magnitude, neurons in the network reach a steady state synchronization level dependent only on the number of neurons in the network, equivalent to the steady state level of uncoupled Poisson neurons. The channel noise only affects the time to reach the steady state synchronization level.
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