Relaxing conjugacy to fit modeling in dynamical systems.
We address a fundamental modeling issue in science as related to the field of dynamical systems: when is a model of a physical system a OgoodO representation? Conjugacy provides a means to determine if two systems are dynamically equivalent. We develop mathematical technology to decide when dynamics of a OtoyO model are like (although not identical to) dynamics of the physical system, since the concept of conjugacy is too rigid for such cases. We contrast the usual methodology where model quality is measured in a Banach space to our dynamically motivated notion of matching orbits as best as possible. We highlight our methods with a lower-ordered model of a "noisy" logistic map and also a simplified model of a Lorenz system such that the usual one-dimensional map model is not exactly justified in the traditional sense.
Skufca
Joseph D
JD
Department of Mathematics, Clarkson University, Potsdam, New York 13699, USA. jskufca@clarkson.edu
Bollt
Erik M
EM