The nonlinear resonance is captured in a canonical normal form for a saddle-“focus”.

A Bifurcation diagram of fixed points of this system, giving rise to a stable focus (red) and an unstable saddle (dotted green). B Top: The bifurcation structure of solutions resulting from non-sinusoidal forcing with f as bifurcation parameter (A = 1). The area between vertical bars contains unstable period-doubled solutions, which is evidence of the existence of a chaotic attractor. Bottom: Inverse of the time T that x needs to reach an absolute value of 106, which is evidence that solutions diverge due to the instability of the chaotic orbit. C Comparison of the nonlinear response of the reduced system (left) with the full system (right). Parameters of normal form: μ = 2, a = 0.4. Parameters of full model: η = −10, , Δ = 2, τ = 20ms.