Bifurcation Analysis of a Van der Pol-Duffing Circuit with Parallel Resistor

Figure 10

Limit cycle created in the Hopf bifurcation for system (1.1) at the point 𝐸₀. The parameter values are 𝜈=3, 𝜇=−0.25, 𝛼=2, and 𝛽=𝛽_1𝑐−0.1=1.9625. Time of integration is [450,750] in (a) and [900,950] in (b). Initial condition is (0.001,−0.001,0.001). Stepsize = 0.1. The point 𝐸₀ is an unstable focus and a limit cycle arises around it. Eigenvalues at 𝐸₀ are 𝜆₁=−2.774,𝜆_2,3=0.012±0.728𝑖.

(a)

(b)