The asymptotic shapes of periodic solutions of a singular delay differential system

f(0, lambda): R --> R be given so that f(0, lambda) = 0 and f(x, lambda) = (1 + lambda) x + ax(2) + bx(3) + o(x(3)) as x --> 0. We characterize those small values of epsilon > 0 and lambda is an element of R for which there are periodic solutions of periods approximately 2/k with k is an element of N of the following system arising from a network of neurons [GRAPHICS] The periodic solutions are synchronized if k is even and phase-locked if k is odd. We show that, as epsilon --> 0, these periodic solutions approach square waves if a = 0 and b < 0, and pulses if a = 0 and b > 0 or if a not equal 0. (C) 2001 Academic Press.