Title :
Nonlinear differential systems: A canonic, multivariable theory
Author :
Newcomb, Robert W.
Author_Institution :
University of Maryland, College Park, MD
fDate :
6/1/1977 12:00:00 AM
Abstract :
An attached (multivariable) nonassociative algebra is shown to be a useful tool for the study of general polynomic differential systems. The main result is that the theory allows the reduction of all such systems to the canonic quadratic form x·= x ċ x within the algebra. This canonic square law differential equation is obtained through multivariable introductions to make all terms quadratic; nonstationary systems are included as are nonpolynomic differential systems through approximation. In the algebra a canonical power series solution is found which is useful for computer aided analysis. Examples are given to illustrate the concepts.
Keywords :
Algebra; Differential algebraic equations; Differential equations; Linear systems; Network synthesis; Nonlinear equations; Polynomials; Stability; Systems engineering and theory; Writing;
Journal_Title :
Proceedings of the IEEE
DOI :
10.1109/PROC.1977.10590
