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

摘要

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