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

Figure 17

Phase portrait of system (1.1) for the parameters at the point 𝑄1=(𝜇_𝑄1,𝜈_𝑄1,𝛽_𝑄1) of Theorem 4.6 in the parameter space: (𝜇,𝜈.𝛽). The solutions near the equilibria 𝐸_± behave like periodic solutions. Time of integration is [10500,12500]. There are several initial conditions. Stepsize = 0.1. There is also a “big” periodic orbit encircling the equilibria 𝐸_±. Eigenvalues at 𝐸₀ are 𝜆₁=0.359,𝜆₂=−1.942,𝜆₃=−0.355. Eigenvalues at 𝐸_± are 𝜆₁=−2.123, 𝜆_2,3=−0.312×10⁻¹⁰±0.483𝑖≈±0.483𝑖.