Several aspects of global dynamics and the existence of periodic solutions are studied for the scalar differential delay equation x′(t) = a(t)f(x([t - K])), where f(x) is a continuous negative feedback function, x · f(x) < 0, x ≠ 0, 0 < a(t) is continuous ω-periodic, [·] is the integer part function, and the integer K ≥ 0 is the delay. The case of integer period x allows for a reduction to finite-dimensional difference equations. The dynamics of the latter are studied in terms of corresponding discrete maps, including the partial case of interval maps (K = 0).
All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics