The authors consider the solutions of the nonlinear equation \(x''+ hx'- x(\kappa- \gamma x^2) = f(\Omega t)\), where \(h\), \(\kappa\) and \(\gamma\) are constants, and \(f(\Omega t)\) is a continuous and periodic function with period \(2\pi\) with respect to \(\Omega t\). An approach is proposed for the determination of the boundary between periodic and aperiodic manifolds of solutions.