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

Abstract

In this paper the focus is set on a modified Chua's circuit model equation with saw-tooth function in place of piece-wise linear function of Chua's circuit displaying multi-scroll chaotic attractors. We study the characteristic properties of first passage times ($t_\mathrm{FPT}$s) to $n$th scroll chaotic attractor, residence times ($t_\mathrm{RT}$s) on a scroll attractor and returned times ($t_\mathrm{RET}$s) to the middle-scroll attractor. $t_\mathrm{FPT}$s exhibit a series of Gaussian-like distribution followed by a long tail continuous distribution. $t_\mathrm{RT}$s and $t_\mathrm{RET}$s show completely discrete distribution. Power-law variation of mean values of $t_\mathrm{FPT}$s, $t_\mathrm{RT}$s and $t_\mathrm{RET}$s with a control parameter 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 scroll attractors for fixed values of the control parameter. For the system with infinite scroll chaotic attractors normal diffusive motion occurs. In the normal diffusion process the mean square displacement grows linearly with time.