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Indexed by:Journal Papers

Date of Publication:2020-01-01

Journal:NEW JOURNAL OF PHYSICS

Included Journals:SCIE

Volume:22

Issue:1

ISSN No.:1367-2630

Key Words:excitable networks; criticality; backtracking activation; non-backtracking matrix; excitatory; inhibitory networks; dynamic range

Abstract: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 stimulus intensities that can be robustly distinguished by the network response, and is maximized at the critical state. In this study, we examine the impacts of backtracking activation on system criticality in excitable networks consisting of both excitatory and inhibitory units. We find that, for dynamics with refractory states that prohibit backtracking activation, the critical state occurs when the largest eigenvalue of the weighted non-backtracking (WNB) matrix for excitatory units, lambda(E)(NB), is close to one, regardless of the strength of inhibition. In contrast, for dynamics without refractory state in which backtracking activation is allowed, the strength of inhibition affects the critical condition through suppression of backtracking activation. As 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, lambda(E)(W), to the other where the critical state is reached when lambda(E)(NB) is close to one. For systems in between, we find that lambda(E)(NB)<1 and lambda(E)(W)>1 at the critical state. These findings, confirmed by numerical simulations using both random and synthetic neural networks, indicate that backtracking activation impacts the criticality of excitable networks.