Detecting stochastic multiresonance in neural networks via statistical complexity measure

Abstract

This paper employs statistical complexity measure (SCM) to investigate the occurrence of stochastic multiresonance (SMR) induced by noise and time delay in small-world neural networks coupled with FitzHugh-Nagumo (FHN) neurons. Our findings reveal that SCM exhibits four local maxima at four optimal noise levels, providing evidence for the occurrence of quadruple stochastic resonances. When time delay $\tau$ is taken into account in the information transmission, under moderate noise levels, SCM shows several local maxima when $\tau =n{T}_e$ with $n$ being a positive integer and $T_e$ being the period of subthreshold signal. This indicates the appearance of delay-induced SMR at the multiples of the period of subthreshold signal. Intriguingly, at low noise levels, a strong coherence between time delay and neuronal firing dynamics emerges at $\tau =n{T}_e-2$ , as confirmed by a series of SCM maxima at these time delays. Furthermore, the study demonstrates that by adjusting the degrees and sizes of small-world networks, as well as the coupling strength, it is possible to optimize the strength of delay-induced SMR, thus maximizing the detection capability of subthreshold signal. The research results may provide us with an effective approach for understanding the role of time delay in signal detection and information transmission.

Figure 1

Dependence of SCM, NSE and SNR with respect to noise intensity is shown in (a–c), respectively; (d) space–time plots with noise intensity $D=0.001$, $D=0.04$, $D=0.08$ and $D=0.14$.

Figure 2

Dependence of SCM and NSE on different noise intensities with respect to time delay, where (a) $D=0.02$, (b) $D=0.04$, (c) $D=0.065$, (d) $D=0.08$ and (e) $D=0.14$.

Figure 3

Space–time plots with different values of time delay under $D=0.02$.

Figure 4

Space–time plots with different values of time delay under $D=0.04$.

Figure 5

Dependence of SCM and NSE on different network parameters with respect to time delay, where (a,b) $k=30$,$N=100$ (c,d) $p=0.15$, $N=100$ (e,f) $p=0.15$, $k=30$.

Figure 6

Dependence of SCM and NSE on different coupling strengths with respect to time delay.