Relative abundance and structure of chaotic behavior: The nonpolynomial Belousov-Zhabotinsky reaction kinetics

We report a detailed numerical investigation of the relative abundance of periodic and chaotic oscillations in phase diagrams for the Belousov-Zhabotinsky (BZ) reaction as described by a nonpolynomial, autonomous, three-variable model suggested by Gyoumlrgyi and Field [Nature (London) 355, 808 (1992)]. The model contains 14 parameters that may be tuned to produce rich dynamical scenarios. By computing the Lyapunov spectra, we find the structuring of periodic and chaotic phases of the BZ reaction to display unusual global patterns, very distinct from those recently found for gas and semiconductor lasers, for electric circuits, and for a few other familiar nonlinear oscillators. The unusual patterns found for the BZ reaction are surprisingly robust and independent of the parameter explored.