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.
Highlights
Synchronization is a basis for a variety of brain functions, such as processing of sensory stimuli,[1,2] formation of memory.[3,4] The abnormal change of synchronizationThis is an Open Access article published by World Scientific Publishing Company
The dependence of synchronization measure R with respect to time delay τ is presented in Fig. 1 for different self-correlation times log10(λ) and strengths A of SW noise
Compared with the case of small self-correlation time λ (such as log10(λ) = −1) or strength A of SW noise, the increase of λ or A of SW bounded noise can result in more synchronization transition as time delay τ is increased
Summary
Synchronization is a basis for a variety of brain functions, such as processing of sensory stimuli,[1,2] formation of memory.[3,4] The abnormal change of synchronization This is an Open Access article published by World Scientific Publishing Company. Delay-induced synchronization transition in neuronal network with sine-Wiener noise improve sub-threshold periodic detection in the FHN neuron.[44] CCSW bounded noises can result in breakup of spiral wave and order-disorder spatial pattern transition.[45] In consideration of the importance of synchronization in brain functions, here we investigate the synchronization and synchronization transition in a small-world neuronal network of delayed FHN neurons subjected to SW bounded noise
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