Synchronization in the Uncoupled Neuron System

Using the model of Hindmarsh–Rose neurons, we study the synchronous behavior of the firing patterns in an uncoupled cell system. In this work, the membrane current I_ext is selected as a controllable parameter, whose initial values for all N cells are set to be near one of the bifurcation points randomly. It is found that the system will show un-synchronous state when the external stimuli is absent, otherwise, full synchrony will appear, even though without any coupling connection among these N neurons, indicating the occurrence of uncoupled synchrony. Moreover, similar behavior could also be observed when these neurons are set to be near other bifurcation points. The synchronous error is calculated for discussing this uncoupled synchrony behavior. Finally, we find that such synchrony may have some inherent relevance with the decrease of phase difference between different cells. Our results suggest that biological neuron systems may achieve an effective response to external feeble stimulus by the mode of uncoupled synchrony instead of only by the coupled scheme.