Chaotic Behavior of the Biharmonic Dynamics System

Figure 12

Evolution of stable and unstable manifolds as a function of the damping force coefficients 𝛿 for 𝑎=1, 𝑏=−1, 𝜀=0.02, 𝜔=1 and two different values of 𝛿 close to the critical value 𝛿₀=0.01823. (a) 𝛿=0.018 (b) 𝛿=0.020, with following initial conditions: 𝜃₀=−1.0572, 𝜃̇₀=0.01, 𝜙₀=𝜋/10 for the area 𝐴₀.

(a)

(b)