Stochastic Resonance in Neural Systems with Small-WorldConnections

Abstract

We study the stochastic resonance (SR) in Hodgkin–Huxley (HH) neuralsystems with small-world (SW) connections under the noise synapticcurrent and periodic stimulus, focusing on the dependence of propertiesof SR on coupling strength c. It is found that there exists a criticalcoupling strength c* such that if c<c*, then the SR can appear onthe SW neural network. Especially, dependence of the critical couplingstrength c* on the number of neurons N shows the monotonic evenalmost linear increase of c* as N increases and c* on the SWnetwork is smaller than that on the random network. For the effect ofthe SW network on the phenomenon of SR, we show that decreasing theconnection-rewiring probability p of the network topology leadsto an enhancement of SR. This indicates that the SR on the SWnetwork is more prominent than that on the random network(p = 1.0). In addition, it is noted that the effect becomes remarkable ascoupling strength increases. Moreover, it is found that the SRweakens but resonance range becomes wider with the increase of c onthe SW neural network.