Collapse of lost solution and chaos in a driven piecewise linear Rayleigh oscillator

摘要

In this paper, we study the response of lost solution generating circuit driven by an extremely small sinusoidal force. The lost solution breaks down by the small perturbation with an amplitude of 10{sup}(-5) and chaos appears. To investigate this phenomena in detail, we propose a piecewise linear circuit with a diode which generates lost solution. It is shown that the roughly simplified 4-segment piecewise linear circuit exhibit nearly the same response as that of the smooth model for the perturbation with an amplitude 10{sup}(-5). To analyze collapse of lost solution and chaos generation rigorously, we consider the case that the diode in the circuit operates as an ideal switch. In this case, Poincare' map is derived rigorously as a one-dimensional map. Chaos generation is well explained by this simplified system.