Firing patterns transition induced by system size in coupled Hindmarsh–Rose neural system

Abstract

The effect of system size on the different dynamical states in coupled cell system is numerically investigated, by using the Hindmarsh–Rose (HR) model. We select the external current as a controlling parameter, for the proper coupling intensity, it is found that the system undergoes the transition of neural firing patterns from one state to another one, when the number of neurons in coupled system is set to be a proper value. And if the coupled system is turned below the bifurcation point, we find that such transition behavior can occur both between two different periodic states, or periodic state and chaotic one. These phenomena imply the occurrence of firing patterns transition (FPT) induced by system size in this coupled system. Furthermore, if we select r as a controlling parameter, we can also find the similar transition behavior can also be observed, and find that such transition behaviors may have some inherent relevance with the activity degree. Finally, we simply gave the reason for difference direction of FPT. Our results indicate the HR system may make an effective response to external stimulus by adjusting itself parameter, and using this transition mode.