NDLI: Global Synchronization and Asymptotic Phases for a Ring of Identical Cells with Delayed Coupling

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Tseng, Jui-Pin Shih, Chih-Wen
Copyright Year	2011
Abstract	We consider a neural network which consists of a ring of identical neurons coupled with their nearest neighbors and is subject to self-feedback delay and transmission delay. We present an iteration scheme to analyze the synchronization and asymptotic phases for the system. Delay-independent, delay-dependent, and scale-dependent criteria are formulated for the global synchronization and global convergence. Under this setting, the possible asymptotic dynamics include convergence to single equilibrium, multiple equilibria, and synchronous oscillation. The study aims at elucidating the effects from the scale of network, self-decay, self-feedback strength, coupling strength, and delay magnitudes upon synchrony, convergent dynamics, and oscillation of the network. The disparity between the contents of synchrony induced by distinct factors is investigated. Two different types of multistable dynamics are distinguished. Moreover, oscillation and desynchronization induced by delays are addressed. We answer two conjectures in the literature.
Starting Page	1667
Ending Page	1697
Page Count	31
File Format	PDF
ISSN	00361410
DOI	10.1137/10080885X
e-ISSN	10957154
Journal	SIAM Journal on Mathematical Analysis (SJMAAH)
Issue Number	4
Volume Number	43
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2011-07-07
Access Restriction	Subscribed
Subject Keyword	delay oscillation synchronization multistability Bifurcation theory neural network Neural biology Neural networks, artificial life and related topics Stability theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis Computational Mathematics

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