A RIGOROUS PROOF OF THE EXISTENCE OF CHAOS IN DOUBLE SCROLL

This paper provides a rigorous mathematical proof that the double scroll is indeed chaotic. Our approach is to derive a linearly equivalent class of piecewise-linear differential equations which includes the double scroll as a special case. The analytical expressions characterizing various half-return maps associated with the Poincare map are used in a crucial way to prove the existence of Shilnikov-type homoclinic orbit, thereby establishing rigorously the chaotic nature of the double scroll. These analytical expressions are also fundamental in our in-depth analysis of the birth (onset of the double scroll) and death (extinction of chaos) of the double scroll.