A singular bifurcation into instant chaos in a piecewise-linear circuit

Strange bifurcation route to chaos is found in a piecewise-linear second-order nonautonomous differential equation derived from a simple electronic circuit. When a limit cycle loses its stability, the attractor changes directly to chaos (instant chaos) without undergoing a period doubling bifurcation or an intermittency. The width of the attractor's band is continuous at the bifurcation point, and the chaotic band grows larger continuously as the system parameter is varied. We call this bifurcation a singular bifurcation into instant chaos. The purpose of this paper is to show that the singular phenomenon arises from the piecewise-linearity of the system. To analyze this phenomenon in detail, the degenerate approach is applied. In this simplified case, the Poincare map is derived rigorously as a one-dimensional mapping. By analyzing it, we prove with computer assistance that the Liapunov exponent jumps discontinuously from minus to plus at the bifurcation point.<
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