BISTABLE CHAOS .2. BIFURCATION-ANALYSIS

Results of a bifurcation analysis are given for the model of a Van der Pol-Duffing autonomous electronic oscillator. The oscillator is described by three ordinary differential equations and consists of a RC oscillator resistively coupled to an LC oscillator. The steady-state problem is described by the unfolding of the quartic potential F = 1/4X4 - 1/2alphaX2 + muX, giving rise to the elementary cusp catastrophe. We show how the bifurcation diagram evolves with mu and recover a "cross-shaped diagram" reminiscent of the one obtained by Boissonade and De Kepper for the Belousov-Zhabotinskii chemical system [J. Phys. Chem. 84, 501 (1980)]. We also show that nonzero values of mu result in coexisting attractors with different dynamics. Specifically, we show a limit cycle attractor in one potential well coexisting with a chaotic attractor in the other well.