Stable control of simple systems is defined by the Nyquist number. The Nyquist number indicates whether the relationship between the control system and deviation causing subsystems or external factors is likely to become stable, oscillatory or trend towards an unstable or even unknown outcome.
In essence, the Nyquist number reflects phase differences between system disturbing activities and the control responses to disturbances, which in turn results in a change to the disturbing activities and further changes in the control responses.
Although the central issue is one of time and lags, by representing the behaviours of disturbance and control in circular form by Fourier transform, the time can be regarded as a difference in phase between a complex Fourier function representing the disturbance and its subsequent modification by the control system and a different complex Fourier function representing the control response.
This axiom focuses on the stability conditions in variety-processing systems through phase relationships between variety generation (disturbance) and control responses. This is extending classical control theory's Nyquist criterion into the variety dynamics framework, providing criteria for conditions for when variety-control feedback loops produce stability, oscillation, or chaos.
Universal pattern: Across all variety-processing systems - biological, economic, social, technological - stability requires maintaining appropriate phase relationships between variety generation and control response.
The mathematics of feedback control (Nyquist) provides a foundation for understanding stability in variety dynamics.