Chaos via torus breakdown

Chaos has been observed from a four-element autonomous circuit whose only nonlinear element is a two-terminal resistor characterized by a three-segment piecewise-linear <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\upsilon-i</tex> characteristic. Both laboratory measurements and computer simulations have confirmed the chaotic behavior to have resulted from the breakdown of a "quasi-periodic" attractor (torus) into a "folded torus." A two-parameter bifurcation diagram is carefully constructed to predict and explain various observed bifurcation phenomena, such as rotation number, devil's staircase, and Arnold tongue.