THEORY AND EXPERIMENTS ON THE EFFECTS OF PERTURBATIONS ON NONLINEAR CHEMICAL-SYSTEMS - GENERATION OF MULTIPLE ATTRACTORS AND EFFICIENCY

Periodic perturbations are applied to the input fluxes of reactants in a system which exhibits autonomous oscillations, the combustion of acetaldehyde (ACH) and oxygen, and a system which exhibits damped oscillations, the combustion of methane and oxygen. The ACH system is studied by experiments and numerical analysis and the methane system is studied by numerical analysis. The periodic perturbations are in the form of a two-term Fourier series. Such perturbations may generate multiple attractors, which are either periodic or chaotic. We discuss two types of bistable responses: a new phase bistability, in which a subharmonic frequency is added to a sinusoidal perturbation at different phases relative to the periodic response; and jump phenomena, in which the resonant frequency of a nonlinear oscillator depends on the amplitude of the periodic perturbation. Both the ACH and the methane systems confirm the phase bistability. The additional complex behavior of bistability due to jump phenomena is seen only in calculations in the methane system. In both types of bistability a hysteresis loop is formed as we vary the form of the periodic perturbation. In the methane system, we find period doubling to chaos occuring on one branch of the hysteresis loop while the other branch remains periodic. The methane system has been studied in the context of the efficiency of power production. We calculate the efficiency corresponding to each bistable attractor and find one branch of each pair to be the more efficient mode of operation. In the case of the coexisting periodic and chaotic attractors the chaotic attractor is the more efficient mode of operation. © 1990 American Institute of Physics.