# Automatic Verification of Dynamical Systems Properties

Wednesday, November 19, 1997 - 3:00pm - 3:30pm

Keller 3-180

R. Baker Kearfott (University of Southwestern Louisiana)

Properties of dynamical systems are often specified by properties of solutions to nonlinear systems of equations. For example, bifurcation points correspond to parameter values in a parametrized nonlinear system where the number of such solutions changes.

With interval computations, computer arithmetic can be used to rigorously prove that such dynamical systems have certain properties. The following contexts will be highlighted:

Incorporation of interval arithmetic in path-following algorithms to verify continuation along a single mathematical path.

Use of interval arithmetic to compute the topological degree of a mapping.

Use of interval arithmetic to verify a particular value of the topological degree of a mapping.

Use of interval arithmetic to rigorously find all solutions to a nonlinear system of equations within a particular region of space (finite or infinite-dimensional).

The relative difficulty and practicality of each of these tasks will be discussed.

With interval computations, computer arithmetic can be used to rigorously prove that such dynamical systems have certain properties. The following contexts will be highlighted:

Incorporation of interval arithmetic in path-following algorithms to verify continuation along a single mathematical path.

Use of interval arithmetic to compute the topological degree of a mapping.

Use of interval arithmetic to verify a particular value of the topological degree of a mapping.

Use of interval arithmetic to rigorously find all solutions to a nonlinear system of equations within a particular region of space (finite or infinite-dimensional).

The relative difficulty and practicality of each of these tasks will be discussed.