Yuming Chen, Jianhong Wu
Jan 20, 2001
Journal of Differential Equations
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.