Statistical measures and diffusion dynamics in a modified Chua's circuit equation with multi-scroll attractors

摘要

In this paper the focus is set on a modified Chua's circuit model equationwith saw-tooth function in place of piece-wise linear function of Chua'scircuit displaying multi-scroll chaotic attractors. We study the characteristicproperties of first passage times ($t_\mathrm{FPT}$s) to $n$th scroll chaoticattractor, residence times ($t_\mathrm{RT}$s) on a scroll attractor andreturned times ($t_\mathrm{RET}$s) to the middle-scroll attractor.$t_\mathrm{FPT}$s exhibit a series of Gaussian-like distribution followed by along tail continuous distribution. $t_\mathrm{RT}$s and $t_\mathrm{RET}$s showcompletely discrete distribution. Power-law variation of mean values of$t_\mathrm{FPT}$s, $t_\mathrm{RT}$s and $t_\mathrm{RET}$s with a controlparameter is found. On the other hand, mean values of $t_\mathrm{FPT}$s and$t_\mathrm{RET}$s have linear dependence with the number of the scrollattractors for fixed values of the control parameter. For the system withinfinite scroll chaotic attractors normal diffusive motion occurs. In thenormal diffusion process the mean square displacement grows linearly with time.