Power law dependence found on the lifetime of a photoconductor chaotic transientnumerically induced by a fixed-step algorithm

Abstract

A direct procedure is proposed to determine whether a chaotic transient is caused by the dynamic of a system or by the numerical artifact employed to solve it. This test is carried out by correlating the resulting lifetimes of the chaotic transients for independent driving parameters of a nonlinear system. In this work the transient behavior of a photoconductor model was investigated for two different parameters such as the capture probability and the trap density. The model was integrated with a conventional fixed-step Runge-Kutta technique, displaying a complex intermittent transient that breaks down through bifurcation reversals into the fixed points of the system. It was found that the corresponding average escape time of these transients follows a power law dependence with the driving parameter, in accordance with the theories of Grebogi, Ott, and York. However, for the two physically independent parameters involved, the average lifetime yielded exactly the same critical exponent. These results directly imply the role of the algorithm as the common underlying source where the chaotic transients are numerically induced, in complete agreement with previous studies on this system.