Abstract
In a previous paper, we discussed the characteristics of a “meaningful” average of a collection of dynamical systems, and introduced as well as contructed a “meaningful” average that is not usually what is meant by an “ensemble” average. We also addressed the associated issue of the existence and construction of such an average for a class of interconnected, linear, time invariant dynamical systems. In this paper, we consider the issue of the construction of a meaningful average for a collection of a class of nonlinear dynamical systems. The construction of the meaningful average will involve integrating a nonlinear differential equation, of the same order as that of any member of the systems in the collection. Such an “average” dynamical system is not only attractive from a computational perspective, but also represents the macroscopic behavior of the interconnected dynamical systems. An average dynamical system can be used in the analysis and design of hierarchical systems.
Discovering time-varying aerodynamics of a prototype bridge by sparse identification of nonlinear dynamical systems
