Existence and determination of super-harmonic synchronizations as solutions of a quasi-linear physical system (Q802331)

Existence of super-harmonic synchronizations of orders 2, 3, and 4 of a quasi-linear physical system described by the quasi-linear differential equations: ẍ\(+k_ 1x+k_ 2f(\Omega t)x^ n=0\), \(k_ 2\ll 1\), for an odd integer n (3 and 5) and a continuous periodic function f(\(\Omega\) t) (sinusoidal function) are proved. Also those synchronizations are determined in the plane \(k_ 1,k_ 2\) for a given initial point \(x_ 0,\dot x_ 0\).