Chaos in a Magnetic Pendulum Subjected to Tilted Excitation and Parametric Damping

Figure 3

Critical amplitude 𝑟 for the appearance of nonperiodic motion as function of the system parameters for 𝜆=0.2, 𝜂=−1, 𝛼=0.075, and 𝛽=0.5. The domain under a line is where a periodic motion is guaranteed. Blue line 𝛾=0, red line 𝛾=𝜋/2, and green line 𝛾=𝜋/4. (a) 𝑟 as function of the driving frequency 𝜔; (b) 𝑟 as function of the tilt angle 𝛾 for 𝜔=1.5.

(a)

(b)