Comparing Regulators: The Homeostat vs. Multiplier Feedback
Ross-Ashby introduced the Homeostat in his book “Design for a Brain” published in 1960. The Homeostat is a system of five motors with sensors and negative feedback randomly coupled to each other. The design senses conditions of instability as the motors turn, whenever instability is detected a new random selection of coupling is used. The selection is repeated quickly and automatically until a stable set of values is selected. The system was dubbed “The Kitten” because it stimulates to a state of instability then seems to search for stability and settles down when it finds it.
Principia Cybernetica describes homeostasis as resistance to change, which agrees with Ashby’s Homeostat models the regulation of disturbances to a living organisms, such as ambient temperature variations in constant temperature animals. Linear negative feedback with an internal set-point is sufficient to describe how Ashby’s homeostat works with temperature regulation but not how the mechanism of hunger leads to a state of satiation. Animal behaviorists understand homeostasis as the regulation of the intake of body needs, such as hunger and thirst. In satiation, an animal does not respond to food stimuli with little effect of its availability or content, if the regulating element were a subtractor as in negative feedback then the animal would need to counter-balance the stimulus internally, which suggests needless processing of information with no physiological evidence of processing. However, if the regulating element was a multiplier then a state of zero hunger in the multiplicand could be reached, which would remove the effect of all feeding stimuli in the sated state.
The analysis of multiplier feedback mechanisms is not new. Frechet and Volterra solved the formal integral equations in the early part of the twentieth century. Numerous contributions ensued, particularly to the Multi Dimensional Laplace Transform which is probably the most practical tool of analysis of the integral equations. Notably, in the 1990’s a form of multiplier feedback structure was used to describe neuron behavior by Kronenburg et al. In order for the multiplier element to describe homeostasis in animal behavior it had to meet certain conditions: A saturation element has to be in the forward path and an inverted even order nonlinear element in the feedback path in order to insure that saturation leads to zero forward gain.
The multiplier feedback could simulate hysteresis in magnetism and other media in a robust analytical way, the structural conditions to be met are slightly different: third order saturation nonlinearity in the forward path and even order non-inverted nonlinearity in the feedback path.
In order to compare the mechanisms of Ashby’s Homeostat and multiplier feedback interactive Java applet simulations will be presented, including multiplier feedback homeostasis and hysteresis.
I am grateful to Dr. Horace Townsend who permitted me to use the Homeostat Java code.