Toward heterogeneity in feedforward network with synaptic delays based on FitzHugh–Nagumo model

Abstract

We focus on the role of heterogeneity on the propagation of firing patterns in feedforward network (FFN). Effects of heterogeneities both in parameters of neuronal excitability and synaptic delays are investigated systematically. Neuronal heterogeneity is found to modulate firing rates and spiking regularity by changing the excitability of the network. Synaptic delays are strongly related with desynchronized and synchronized firing patterns of the FFN, which indicate that synaptic delays may play a significant role in bridging rate coding and temporal coding. Furthermore, quasi-coherence resonance (quasi-CR) phenomenon is observed in the parameter domain of connection probability and delay-heterogeneity. All these phenomena above enable a detailed characterization of neuronal heterogeneity in FFN, which may play an indispensable role in reproducing the important properties of in vivo experiments.

Practical dynamic consensus of Stuart–Landau oscillators over heterogeneous networks

“…In its simplest form, consensus consists in a group of linear interconnected systems synchronizing their trajectories and asymptotically reaching a common equilibrium point determined by the systems' intial conditions (Olfati-Saber & Murray, 2004;Ren et al, 2007). Furthermore, when the network is heterogeneous, that is, when it comprises systems with different dynamics and/or different parameters, it is possible that consensus is not reached, but a steady-state error may prevail -see e.g., Qin et al (2018); Steur et al (2016); Wang et al (2015); Zhang et al (2016). This may be referred to as practical consensus.…”