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

Figure 11

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−1=1.0625 in (a); 𝛽=𝛽_1𝑐−2=0.0625 in (b). Time of integration is [0,150] in (a) and [0,100] in (b). Initial condition is (0.001,−0.001,0.001). Stepsize = 0.1. As the parameter 𝛽 stay away from the critical value 𝛽_1𝑐 the solutions tend faster to the limit cycle. Eigenvalues at 𝐸₀ are (a) 𝜆₁=−2.985, 𝜆_2,3=0.117±0.502𝑖; (b) 𝜆₁=−3.203, 𝜆₂=0.418, 𝜆₃=0.034.

(a)

(b)