On Offset Boosting in Chaotic System

Abstract

Offset boosting is an important issue for chaos control due to its broadband property and polarity control. There are two main approaches to realize offset boosting. One is resort to parameter introducing where an offset booster realizes attractor boosting. The other one is by the means of periodic function or absolute value function where any self-reproduced or doubled attractors with diverse offset are extracted out by a specific initial condition. The former also provides a unique window for observing multistability and the latter gives the direction for constructing desired multistability.

Complex dynamics analysis and feedback control for a memristive switched chaotic system

“…The variable signals that realize the offset boosting in this way are often unique. Chunbiao Li [37] discussed the combination scheme of offset boosting induced by constant and periodic functions, where the periodic function is related to the system variabley. In this section, we will discuss the combination scheme of constant and switching functions, and the switching function is independent of the system variable.…”

“…For example, offset boosting has been found in conservative chaotic systems [30][31][32], fractional-order chaotic systems [33], discrete chaotic systems [34,35], and HR neuron models [36]. In 2021, Chunbiao Li et al concluded two methods to realize offset boosting, one is based on introducing a control constant, and the other is adding periodic trigonometric or absolute value functions and then changing the initial values of the system [37]. Inspired by periodic trigonometric functions, researchers introduced memristors with sinusoidal or cosinusoidal conductance into the dynamical system and also discovered offset boosting behavior [38,39].…”

Adjustable symmetry on the dynamics of a new chaotic system with cyclic symmetry: theoretical study, control and experimental investigation

“…We also consider the offset boosting phenomenon based on the increase of a constant in the nonlinearity and the associated variables depending on the choice of the offset variable [23,24]. Thus we apply this method on cyclic system (1) and we obtain the following system (6):…”

Autonomous piecewise damping Josephson junction jerk oscillator: microcontroller implementation, controls, and combination synchronization

“…This is achieved with methods including time-reversible symmetry [46], attractor self-reproducing [47], attractor doubling [48], repellor construction [49], and conditional symmetry [50]. Continuous models and discrete maps are some domains of concern where offset boosting has been employed with increasing research explorations as cited by Li et al [51] and the citations therein. In the recent literature, Kingni et al [52] exposed an autonomous 5D complex system with offsetboosting controls.…”