The piecewise-linear Lorenz circuit is chaotic in the sense of Shilnikov

The authors prove that the piecewise-linear Lorenz circuit is chaotic in the sense of Shilnikov. They first prove the existence of a heteroclinic orbit, and then prove an inequality among the eigenvalues. In addition to a detailed analysis of the piecewise linear dynamics, interval analysis is utilized to prove various inequalities. This novel approach can be applied to many other problems that require proving rigorously the existence of either a homoclinic or a heteroclinic orbit. With this proof, the piecewise-linear Lorenz circuit becomes one of the very few real physical systems where chaos has been observed by laboratory measurement, confirmed by simulation, and proved mathematically