Nonlinear Dynamics of a Periodically Driven Duffing Resonator Coupled to a Van der Pol Oscillator

Figure 10

Van der Pol oscillator (b) is synchronized to the Duffing resonator (a) and behaves like a normal Duffing resonator showing a hysteresis curve and jumping phenomena when Ω varies between 0.6 and 1.4 with the initial conditions of 𝑥₁(0)=1, 𝑥̇₁(0)=0, 𝑥₂(0)=0, 𝑥̇₂(0)=0 and the parameters of the system are, respectively, 𝑐₁=0.1, 𝑐₂=0.05, 𝑘₃=0.3, 𝑘_𝑐=8, and 𝑓_𝑑=0.2.

(a)

(b)