Abstract
The differential equation of the sinusoidally forced pendulum is studied by digital simulation in a régime where two simple, symmetrically related chaotic attractors grow and merge continuously as the forcing amplitude is increased. By introducing a small constant bias in the forcing to break the symmetry, two discontinuous bifurcations unfold from the single merging event. Considering both forcing amplitude and bias together as controls, a codimension two bifurcation of chaotic attractors is defined, whose geometric structure in control-phase space is closely related to the elementary cusp catastrophe. The chaotic bifurcations are explained in terms of homoclinic structures (Smale cycles) in the Poincaré map.
Reference28 articles.
1. Abraham R. H. 1985 Chaostrophes intermittency and noise. In Chaos fractals and Dynamics (ed. P. Fischer & W. R. Smith) pp. 3-22. New York: Marcel Dekker.
2. Abraham R. H. & Shaw C. D. 1982-8 Dynamics: The geometry of behavior: part 1; Periodic behavior (1982); part 2 Chaotic behavior (1983); part 3 Global behavior (1985); part 4 Bifurcation behavior (1988). Santa Cruz: Aerial Press.
3. Benedicks M. & Carleson L. 1988 The dynamics of the Henon map. Preprint.
4. Birkhoff G. D. & Smith P. A. 1928 Structure analysis of surface transformations. J. Math appl. 7 345-379.
5. The dynamics of phase locking and points of resonance in a forced magnetic oscillator
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