Stochastic Stability of Damped Mathieu Oscillator Parametrically Excited by a Gaussian Noise

Figure 3

First moment stability: plot of 𝑆_cr as function of Ω according to (3.12) for 𝜔₀=2π, 𝜁₀=0.05, and𝛽=𝜅𝛿/(𝜔₀Ω) with 𝜅=4.01 (red line), 4.10 (black), 4.5 (blue), and 5.0 (violet).

(a)

(b)