Chemical oscillators periodic perturbation

Schneider, F. W. (1985). Periodic perturbations of chemical oscillators experiments. Ann. Rev. Phys. Chem., 36, 347-78. 

In these experiments, the volume of the confined gel is constant its main role is to damp hydrodynamical motions that would otherwise perturb the chemical intrinsic patterns. More recently it has been shown experimentally that the coupling of a volume phase transition with a chemical oscillator can generate a self-oscillating gel (i, 4). More precisely, if one of the chemical species taking part in the chemical reaction modifies the threshold for the phase transition, then the time periodic variation of this concentration can generate autonomous swelling-deswelling cycles of the gel even in absence of any external stimuli (5, 6). This device thus provides a novel biomimetic material with potential biomedical and technical applications. 

It means that one component is perturbed by amplitude a, a cosinusoidal forcing term with frequency co and phase (p. Recently particular attention has been paid to the response of nonlinear chemical oscillators that are periodically perturbed. The celebrated Brusselator model... 

Rehmus, Ross, J. (1984). Periodically perturbed chemical systems. In Oscillations and travelling waves in chemical systems, eds R. J. Field M. Burger, pp. 287-332. John Wiley, New York. 

It is worth asking whether perturbation methods might yield as much or more information about oscillating reactions, where it might be possible to probe not only constant or monotonically varying concentrations but also amplitude and phase relationships. Schneider (1985) reviewed a variety of model calculations and experiments on periodically perturbed chemical oscillators. The results, which show such features as entrainment, resonance, and chaos, are of considerable interest in the context of nonlinear dynamics, but shed little light on the question of mechanism. 

With the aim in mind to clarify the still existing problems we examined how the characteristics of chemical oscillation /e.g. period time, amplitude/ are altered by the addition of bromocomplex-forming ions [thallium/III/, mercury/Il/3 to the reacting systems. For, these ions perturb the dynamic bromide concentration conditions prevailing in bromate oscillators [3]. 

The study of the response of nonlinear systems to external periodic perturbations leads to interesting information.Cool-flame, 9 oscillations occur in a number of combustion reactions, and we discuss an experimental study of the effect of external periodic perturbations on such systems. The application of perturbations to a chemical reaction can reveal important information about the stability, kinetics, and dynamics of the reaction. This technique is well known in the field of relaxation kinetics, in which perturbations are applied to a chemical system at equilibrium. In our work, periodic perturbations are first applied to the input rates of acetaldehyde and oxygen, one at a time, in the combustion of acetaldehyde in a CSTR. We measure periodic responses in five entrainment bands as we vary the frequency and amplitude of the external periodic perturbation. Outside of entrainment bands we find quasi-periodic responses. Next-phase rnapslO, of the experimental results are constructed in real time and used in the observation and interpretation of entrainment and quasi-periodic behavior. Within the fundamental entrainment band, we measure critical slowing down and enhancement of the response amplitude. As the bath temperature is increased, so that the oscillatory system approaches a Hopf bifurcation, we observe an increase in the amplitude enhancement. The predictions of a five-variable thermokinetic model agree well with the experimental results. 

Sound waves provide a periodic oscillation of pressure and temperature. In water, the pressure perturbation is most important in non-aqueous solution, the temperature effect is paramount. If cu (= 2 nf, where/is the sound frequency in cps) is very much larger than t (t, relaxation time of the chemical system), then the chemical system will have no opportunity to respond to the very high frequency of the sound waves, and will remain sensibly unaffected. 

The Lotka-Volterra type of equations provides a model for sustained oscillations in chemical systems with an overall affinity approaching infinity. Perturbations at finite distances from the steady state are also periodic in time. Within the phase space (Xvs. Y), the system produces an infinite number of continuous closed orbits surrounding the steady state... 

While it remains extremely difficult to pinpoint the origin of chaos in any particular experiment, it now appears that chemical chaos in the BZ reaction can result either from the homogeneous chemistry or from perturbation of that chemistry under periodic oscillating conditions by the effects of imperfect mixing. 

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