Periodic offset boosting for attractor self-reproducing

The special regime of multistability of attractor self-reproducing is deeply decoded based on the conception of offset boosting in this letter. Attractor self-reproducing is essentially originated from periodic initial condition-triggered offset boosting. Typically, a trigonometric function is applied for attractor self-reproducing. The position, size, and clone frequency determine the selected periodic function. Specifically, in-depth investigation on three elements of sinusoidal quantity is taken into account and then a universal law of attractor self-reproducing is built: the original position of an attractor determines the initial phase and the size of attractor sets the amplitude, while the reproducing interval between two attractors determines the frequency of the trigonometric function. It is found that the product of amplitude and frequency is a constant determined by the reproducing periodic function. The positive and negative switching of the slope in sinusoidal function also leads to the waste of phase space since in general there is no attractor reproduced at the region with negative slope except that new polarity balance is reconstructed paying back the attractor with conditional symmetry. Three-element-oriented offset boosting makes attractor self-reproducing more designable, achievable, and adjustable, which brings great convenience to engineering applications.