Research On Critical Behavior Of Excitable Neural Networks

The exploration of the operation mechanism of neural networks,especially the information transmission mechanism between neurons,is of great significance for understanding human cognitive behavior.As a discrete model of information transmission between neurons,networks of excitable elements are widely used to model real-world biological and social systems.The dynamic range of an excitable network quantifies the range of external stimulus intensities that can be robustly distinguished by the network response.When the network reaches the critical regime,the dynamic range is maximized.This paper mainly examines the impacts of backtracking activation on system criticality in excitable networks that contain both excitatory and inhibitory units.The results show that,for dynamics with refractory states that prohibit backtracking activation,regardless of how the strength of inhibition changes,the critical state occurs when the largest eigenvalue of the weighted non-backtrackting(WNB)matrix of excitatory units,?NBE,is close to one.On the contrary,for dynamics without refractory state that allows backtracking activation unconditionally,the strength of inhibition affects the critical condition through suppressing backtracking activation.As the inhibitory strength increases,backtracking activation is gradually suppressed.Accordingly,the system shifts continuously along a continuum between two extreme regimes-from one where the criticality is determined by the largest eigenvalue of the weighted adjacency matrix for excitatory units,?WE,to the other where the critical state is reached when ?NBE is close to one.For systems in between,we find that ?NBE<1 and?WE>1 at the critical state.In this paper,these results are confirmed by numerical simulation in random and synthetic networks,highlight the important role of backtracking activation.It is shown that the backtracking activation does affect the criticality of excitable networks.