When we think of oscillators it is natural to consider electronic circuits. In an electronic oscillator there is usually a tuning element selecting some frequency, an amplifier and a feedback mechanism taking some of the amplified signal and feeding it back to the beginning with some phase. If the phase, denoted as positive or negative, is correct then oscillation will occur. We may think of feedback in the following way. Feedback is a situation where a latter step influences an initial step. This is illustrated in the schematic below.
In this circuit A represents the amplification factor of the amplifier and +/-B the gain and phase of the feedback circuit. For positive feedback B is negative leading to oscillations. A little algebra shows the origin of the gain G of the amplifier/oscillator. The amplifier multiplies the total input voltage, composed of input plus feedback, by A yielding the output voltage as shown below.
The negative sign, or positive feedback, gives a small denominator leading to very high gain and ultimately oscillations. This circuit looks to be made of two simple kinetic steps formed from an amplifier and a feedback circuit. No chemical analog is so simple. Chemical oscillators are, in every case, formed by many kinetic steps. When asked recently what are the fewest number of chemical steps to form a chemical oscillator John Ross said that while there was no proof it was probably three. We may think of chemical feedback by virtue of a later chemical step (product) influencing an initial step (the product occuring as a reactant) leading to autocatalysis.
There is one thing we can understand from the electrical circuit and that is that something that alters the feedback gain (i.e. in a chemical reaction, the rate constant) or its phase (in a chemical system it might be a reaction pathway) will affect the ability of the oscillator to oscillate.
There is an important distinction to make between the usual electronics analog of a feedback oscillator which usually has smooth, sinusoidal oscillations and what are calledreaction oscillators where more complicated, even discontinuous, wave forms occur. The Belusov-Zhabotinsky reaction is an example of a reaction oscillator as a study of its wave form will show.
The B-Z reaction more closely resembles an astable multivibrator used in the electronics of counting circuits. The figure below shows a couple of amplifiers fed by two feedback, or coupling circuits. There are two stable states; one with V1 conducting and V2 off and the other with V1 off and V2 conducting.
If both V1 and V2 are "on" then an oscillating condition results. The frequency stability of this oscillator is poor. That is to say, there are excursions in frequency of the "flip flops" between V1 and V2. When viewed from the theory of chaos this electrical circuit begins to look like a member of a class of phenomena having random looking excursions in a region-in this case a frequency domain.