Bifurcation Analysis of a Van der Pol-Duffing Circuit with Parallel Resistor
Figure 4
(a) Typical points , , , , , and in the parameter space near the point . (b) Phase portraits of system (1.1) for the flow restricted to the center manifold and its continuation. For parameters at the equilibrium is unstable; for parameters at the equilibrium is an weak unstable focus (Hopf point with positive); for parameters at the equilibrium is stable and an unstable limit cycle appears from a Hopf bifurcation; for parameters at the equilibrium is an weak stable focus (Hopf point with negative) and there is an unstable limit cycle; for parameters at the equilibrium is unstable and a stable limit cycle appears from a Hopf bifurcation, so there are two limit cycles encircling the equilibrium; for parameters at the equilibrium is unstable and the two cycles collide corresponding to a nondegenerate fold bifurcation of the cycles.
