The existence of positive periodic solutions for periodic feedback control systems with delays

where τ, δ, a, b, c, r, k ∈ C(R, (0,∞)) are ω-periodic functions. The assumption of periodicity of the parameters a(t), b(t), c(t), k(t), r(t) is a way of incorporating the periodicity of the environment (e.g. seasonal effects of weather condition, food supplies, temperature, etc.). The main purpose of this paper is to establish the existence of a positive periodic solution of system (2), using Mawhin’s continuation theorem [2]. For the work concerning the existence of a periodic solution of delay differential equations, which was done by using coincidence degree theory, we refer to [3–5] and references cited therein.