The Asymptotic Shapes of Periodic Solutions of a Singular Delay Differential System
Yuming Chen, Jianhong Wu
Jan 20, 2001
Citations
33
Citations
Journal
Journal of Differential Equations
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Key Takeaway Key Takeaway: Periodic solutions of a neural network can be synchronized or phase-locked, with e0 causing square waves if a=0 and b=0 or a0.
Abstract
Let f(·, λ): R→R be given so that f(0, λ)=0 and f(x, λ)=(1+λ) x+ax2+bx3+o(x3) as x→0. We characterize those small values of e>0 and λ∈R for which there are periodic solutions of periods approximately 2k with k∈N of the following system arising from a network of neurons[formula] The periodic solutions are synchronized if k is even and phase-locked if k is odd. We show that, as e→0, these periodic solutions approach square waves if a=0 and b 0 or if a≠0.
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