When we think of cyclical variations, or oscillations, it is natural to consider electronic circuits as analogs. 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 when -AB = 1. This circuit looks to be made of two simple kinetic steps formed from an amplifier and a feedback circuit. No chemical, or geological 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 called reaction oscillators where more complicated, even discontinuous, wave forms occur. The global temperature variations over time look more like an example of a reaction oscillator.The point of all this is to attempt to build a model of global warming. Even if we do not have the understanding to build an accurate model we can at least have a mental picuture and some language with which to discuss the elements of the phenomena.
Global temperature variations more closely resemble 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.
In creating a model to reflect the variations of global temperature change we want to start "simple." We know that the real, global situation is complicated and not understood. What we want, as in any model, is to capture the gross features and then build in the complicated stuff later. In this spirit, it is global temperature that is the analog of electrical voltage. What is the "gain element," the amplifier in our model?
It is obvious that the "amplifiers" are highly non-linear. In an Hi-Fi amplifier the electrical engineer works hard to achieve linear behavior (using negative feedback in the amp chain to lower distortion). Nature is not so kind since everything seems to be non-linear and complicated and so our model, as it incorporates more detail, will no doubt become more non-linear. In other words, at the start a simple model may yield regular oscillations of temperature and as it becomes more realistic may show more non-linear variations. Lets try and create the elements of a model in words and symbols.