A Chaotic Chemical Reactor With and Without Delay: Bifurcations, Competitive Modes, and Amplitude Death

Abstract

Bifurcations in Huang’s chaotic chemical reactor leading from simple dynamics into chaotic regimes are considered. Following the linear stability analysis, the periodic orbit resulting from a Hopf bifurcation of any of the six fixed points is constructed analytically by the method of multiple scales, and its stability is determined from the resulting normal form and verified by numerical simulations. The dynamically rich range of parameters past the Hopf bifurcation is next explored. In order to bring some order to the search for parameter regimes with more complex dynamics, we employ the recent conjecture of Competitive Modes to find chaotic parameter sets in the large multiparameter space for this system. In addition, it is demonstrated that, by changing the point of view, one may tightly localize the chaotic attractor in shape and location in the phase space by mapping the Competitive Modes surfaces geometrically. Finally, we consider the effect of delay on the system, leading to the suppression of the Hopf bifurcation in some regimes, and also all of the subsequent complex dynamics. In modern terminology, this is an example of Amplitude Death, rather than Oscillation Death, as the complex system dynamics is quenched, with all the variables additionally settling to a fixed point of the original system.