| This work is intended to contribute to a program of developing general concepts and methods for applying category theory to the modeling and solution of scientific problems. It was motivated by my experiences as an engineering student studying continuum and kinetic models of fluid flows. The language of category theory is employed because it facilitates precise comparisons between diverse types of structures. Using this language to investigate relationships between fluid flow models requires categorical specifications of constitutive relations and of idioms occurring across classifications of dynamic systems.; It is shown that a category-theoretic definition of chaotic system applies not only to the Smale horseshoe, a standard chaotic system, but also to Conway's “Game of Life” automaton. Symbolic dynamics of the “Dining Philosophers” relational system is computed. A category composed of stochastic matrices is defined and some of its elementary properties are developed. A categorical variant of symbolic dynamics is applied to a finite stochastic process. Using point-wise Kan extension formulas, conditions ensuring existence of certain representations among categories of dynamic systems are proved. |
