## ABSTRACT

Nonlinear dynamical systems (NOS) theory is an agglomeration of several lines of mathematical thinking. The principal ideas concerning stability, instability, and chaos can be traced to the work of French mathematician Henri Poincare, who worked in the late 19th and early 20th century. Poincare's contributions necessarily built on the work of the greatest earlier giants of mathematics, Newton and Leibnitz, who developed calculus in the middle 17th century, and Laplace, who extended Newton's concepts of determinism in the early 19th century.