Equivalent Mathematical Representation of Second-Order Damped, Driven Nonlinear Oscillators

Figure 8

Amplitude-time, phase plane, and Morlet CWT diagrams for the system parameter values of𝜈=0.2, 𝐴=2, 𝐵=5, 𝜅=0.15, 𝜔_𝑓=0.5, and 𝑄=5 with 𝑥₁₀=1 and 𝑥̇₁₀=1. Here, the dashed black and red lines represent the numerical integration solutions of (34) and (39), while the blue dots describe the numerical integration solution of (37). Similarly, in (b) the black solid line and the red dots represent the numerical integration solutions computed respectively, from (34) and (37).

(a)

(b)

(c)