Delay-induced synchronization transition in a small-world neuronal network of FitzHugh–Nagumo neurons subjected to sine-Wiener bounded noise

Abstract

Noise and delay are ubiquitous in brain and they have significant effects on neuronal network synchronization and even brain functions. Based on a small-world neuronal network of delayed FitzHugh–Nagumo (FHN) neurons subjected to sine-Wiener (SW) bounded noise, the effects of delay and SW noise on synchronization and synchronization transition are numerically investigated by calculating a synchronization measure R and plotting spatiotemporal patterns. The phenomenon of delay-induced synchronization transition is observed as delay [Formula: see text] is increased. And large self-correlation time and strength of SW noise can increase the number of delay-induced synchronization transition. In addition, delay-induced synchronization transition is robust against the change of topology structure of neuronal network and this phenomenon becomes much easier to see for small nearest neighbors k in the small-world network. Since synchronization transition may imply functional switch, our results may have important implications, and inspire future studies.

Lag Synchronization of Noisy and Nonnoisy Multiple Neurobiological Coupled FitzHugh–Nagumo Networks with and without Delayed Coupling

“…In past research, researchers have investigated the interaction between neurons and their networks in different brain regions using techniques like neuroimaging systems [ 56 – 59 ] and used computational models to predict the complex dynamics of neurons [ 60 , 61 ] and showed that noise plays an important role in the dynamical functionality of the neurons and their networks [ 62 , 63 ]. The fundamentals of the noise and delay in the communication of neuronal networks are still ubiquitous but they have a very strong implication for the functionality of neurons and their networks and in general, the synchronized functionality of the brain [ 64 , 65 ]. The noise has a tremendous effect as amplification of the weak neuronal signal and therefore enhances the detection of useful information in the signal [ 64 ].…”

“…The fundamentals of the noise and delay in the communication of neuronal networks are still ubiquitous but they have a very strong implication for the functionality of neurons and their networks and in general, the synchronized functionality of the brain [ 64 , 65 ]. The noise has a tremendous effect as amplification of the weak neuronal signal and therefore enhances the detection of useful information in the signal [ 64 ]. The addition of noise in such networks/systems has unveiled hidden facts such as the development of the stochastic methodology to understand respective resonance [ 66 ], noise sustained synchronization [ 67 ], vibrational resonance [ 68 , 69 ], chaotic resonance [ 70 ], and coherent-resonance [ 71 ] in nonlinear dynamical systems.…”

Synchronization and Rhythm Transition in a Complex Neuronal Network

“…Mostly, the small-world network has been considered as the neuronal system since proposed by Watts and Strogatz in 1998 [36], [37]. In addition, studies have proven that the human brain cortex has small-world properties [12], [16], [33], [35], [38]. The small-world model provides a powerful tool to investigate the structures and dynamics of the human brain.…”

“…The small-world model provides a powerful tool to investigate the structures and dynamics of the human brain. A lot of work concerned the neuronal dynamics of small-world networks [16], [38], [39]. Qu and Wang have explored the synchronization and spatiotemporal behaviors of small-world neuronal networks based on different neuron models [13], [22], [33], [34].…”

Effects of temporally correlated noise on coherence resonance chimeras in FitzHugh-Nagumo neurons

“…Many networks are used to simulate computation. According to the random connection probability, there are regular networks, small world networks and random networks [41,42]. From the perspective of the network topology, the common rule networks have local (nearest neighbor), global (all-to-all), non-local connections [43,44].…”