Many dynamical systems are nonlinear. It is often very challenging to obtain a solution in time domain, which sometimes only has limited significance when it comes to fundamental relationships between system parameters and state variables. Additionally many nonlinear systems usually lead to limit cycles, which represent a periodic solution of the steady state. One very efficient way to approximate it, is the method of the Harmonic Balance. In practice, however, many of the system parameters used are uncertain, but their variation can have serious influences on the existence, type of stability and also amplitudes of the limit cycles. Against this background, it is very desirable to link the model worlds of the approximation of nonlinear oscillations and uncertain quantification (UQ). In UQ the generalized Polynomial Chaos (gPC) is a well known concept, which we combine with the Harmonic Balance to form the generalized Harmonic Balance Polynomial Chaos (gHBPC) Expansion. Initial work on the combination has been published in [1] and shows an efficient way to treat such problems. In this work the gHBPC is initially applied as a benchmark to the forced Duffing oscillator. It already shows special properties in the area of multiple solutions. Based on this, a system of greater complexity is presented. This is a well-known model from cell biology in which highly non-linear electrophysiological processes are closely linked to diffusive processes [2]. The resulting limit cycles are the result of different types of Hopf bifurcations, on which the uncertainty of system parameters has a significant influence.