Formulation of state equations ot general nonlinear systems of multiterminal components

A topological approach to the formulation of state equations for quite general classes of nonlinear dynamical systems of lumped multiterminal components is developed. Three examples, drawn from diverse fields, demonstrate that the state equations form a ´natural´ mathematical model for dynamical analysis. The general theory developed is applicable to a great many physical systems, including the special case of networks comprising linear or nonlinear, passive or active components. The formulation technique is also extended to the systems in which some or all of the components are described by parametric equations. Certain sufficiency conditions are stated in the form of three assertions; one of these could be applied to ensure the existence of the state model in a specific case study.