Crisis of Transient Chaos

A new kind of crisis, which is marked by a sudden change of a strange repeller, is observed in an electronic relaxation oscillator. Firstly, by its simplified piecewise linear model, we show analytically that a strange repeller appears after a hole-induced crisis, and that the fractal dimension of the strange repeller and the averaged lifetime of the iterations in the region occupied by the original attractor suddenly change at the critical parameter value when the repeller disappears. Our numerical investigation convinces us that the corresponding phenomenon can be found in the original electronic relaxation oscillator.