Effect of topology on delay-induced multiple resonances in locally driven systems

Abstract

Information transmission delays are inherent in neuronal systems and significantly influence their dynamic properties. Recent studies have shown that delay-induced multiple resonances occur when delays in synaptic transmission are taken into account. We reveal the influence of topology on the delay-induced multiple resonances phenomenon in locally driven systems in this paper. It is expressed as the maximum value of the Fourier coefficient, which occurs at an integer multiple of T/N, where T is the external signal period or the neuronal intrinsic oscillation period, N is determined by the topology of the network. We briefly discuss the obtained results with the underlying reasons in terms of the network’s topology. The emergence of delay-induced multiple resonances depends on the interaction of the delay enhancement effect and the delay inhibition effect. In the case of weak coupling, the signal response performance is enhanced over a wider range of delay windows, which is dominated by delay enhancement effects. These results may provide a novel perspective on weak signal response and transmission in delay-coupled neural networks.