On the affine nonlinearity in circuit theory

Abstract:
Affine dependence represents a well definable and most commonly met nonlinearity to which, however, usually, no attention is paid. In fact, this nonlinearity exists only in system theory and is linearity in analytical geometry, which is explained by the fact that circuit's power-activity has no direct analogy in the geometry. We also associate ([1], these Proceedings) the affine nonlinearity (ANN) of some 1- ports, obtained via deriving and mutually connecting Thevenin's equivalents, with an analysis of the "structural complexity" (i.e. "entropy") of a system. The Thevenin's contraction is thus used in [1] as some repeatable operation associated with an (algebraic) ideal in a circuit modeling of the growing of some biological structures.