Spike-train bifurcation scaling in two coupled chaotic neurons

We investigate the variation of the out-of-phase periodic rhythm produced by two chaotic neurons (Hindmarsh-Rose neurons [J. L. Hindmarsh and R. M. Rose, Proc. R. Soc. London B 221, 87 (1984)]) coupled by electrical and reciprocally synaptic connections. The exploration of a two-parametric bifurcation diagram, as a function of the strength of the electrical and inhibitory coupling, reveals that the periodic rhythms associated to the limit cycles bounded by saddle-node bifurcations, undergo a strong variation as a function of small changes of electrical coupling. We found that there is a scaling law for the bifurcations of the limit cycles as a function of the strength of both couplings. From the functional point of view of this mixed typed of coupling, the small variation of electrical coupling provides a high sensitivity for period regulation inside the regime of out-of-phase synchronization.