Effects of refractory period on dynamical range in excitable networks**Project supported by the National Natural Science Foundation of China (Grant No. 11675096), the Fundamental Research Funds for the Central Universities of China (Grant No. GK201702001), and the Fund for the Academic Leaders and Academic Backbones, Shaanxi Normal University of China (Grant No. 16QNGG007).

Abstract

Effects of refractory period on the dynamical range in excitable networks are studied by computer simulations and theoretical analysis. The first effect is that the maximum or peak of the dynamical range appears when the largest eigenvalue of adjacent matrix is larger than one. We present a modification of the theory of the critical point by considering the correlation between excited nodes and their neighbors, which is brought by the refractory period. Our analysis provides the interpretation for the shift of the peak of the dynamical range. The effect is negligible when the average degree of the network is large. The second effect is that the dynamical range increases as the length of refractory period increases, and it is independent of the average degree. We present the mechanism of the second effect. As the refractory period increases, the saturated response decreases. This makes the bottom boundary of the dynamical range smaller and the dynamical range extend.