Transmission delay induced criticality in spiking neuronal networks and its filtering effect

Linfeng Wei, Shasha Liu, Yanmei Kang and Ziheng Xu

Chaos, Solitons & Fractals, 2026, vol. 202, issue P1

Abstract: The aim of this paper is to disclose whether the transmission delay can induce criticality using globally coupled spiking neuronal network with delayed feedback. First, the evolutionary equation for the averaged membrane potential is achieved under mean-field approximation. And then the Hopf bifurcation of the mean-field model is acquired by means of central manifold theorem and norm form theory. With bifurcation analysis of the mean-field model as guide, seeking the criticality of the large-scale finite sized network is facilitated. Across the criticality it is found that the population activities of the network undergoes a phase transition from less ordered spiking into more ordered spiking. Furthermore, an enhanced response which resembles the phenomenon of aperiodic stochastic resonance is observed, where the optimal value of the transmission delay is found nearly the same as its critical value. Finally, the functional role of the neuronal network at the critical state is revealed by a biologically inspired image denoising procedure.

Keywords: Critical dynamics; Transmission delay; Mean-field analysis; Hopf bifurcation; Aperiodic stochastic resonance (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:202:y:2026:i:p1:s0960077925014663

DOI: 10.1016/j.chaos.2025.117453

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