Author’s abstract: “We construct two simple examples of strongly monotone time-periodic dynamical systems (of period \(\tau>0)\) possessing linearly stable subharmonic orbits of period \(n\tau\) for any integer \(n\geq 2\). The first example is an irreducible cooperative system of four ODE’s that models positive feedback. The second example is a one- dimensional reaction-diffusion PDE with periodic boundary conditions. Our construction employs Chebyshev’s polynomials”.