Hidden Attractors with Conditional Symmetry

Li, Chunbiao; Sun, Jiayu; Sprott, Julien Clinton; Lei, Tengfei

doi:10.1142/s0218127420300426

Cited by 25 publications

(12 citation statements)

References 45 publications

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“…Moreover, the offset boosting can introduce polarity reversal leading to other regimes of systems with coexisting attractors if the polarity balance is maintained typically conditional symmetry is expectable (Li et al 2020c). Revising the original system to be,…”

Section: Polarity Control Based On Offset Boostingmentioning

confidence: 99%

“…However, offset boosting is such an important issue in chaotic system since that it gives a direct way for an engineer to transform a bipolar chaotic signal to a unipolar one. And besides this, it seems that offset boosting shows more varieties than our imagination such as attractor boosting, attractor self-reproducing (Li et al 2017a), attractor doubling (Li et al 2019), conditional symmetry (Li et al 2020c), time-reversible symmetry (Li and Sprott 2017) or even repellor construction (Li et al 2021). For this reason, offset boosting has attracted great interests recently both in continuous system and in discrete maps.…”

Section: Introductionmentioning

confidence: 99%

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On Offset Boosting in Chaotic System

Jiang

2021

Chaos Theory and Applications

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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.

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Section: Polarity Control Based On Offset Boostingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Offset Boosting in Chaotic System

Jiang

2021

Chaos Theory and Applications

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“…Increasing in the literature of dynamical models, engineering applications targeting the rescaling of dynamical behaviors considering their amplitude modifications is termed offset boosting, which is the change in coordinate point of chaotic attractors with the goal of redesigning and the conditioning of signal of equivalent unipolar ones from their bipolar chaotic counterparts. 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.…”

Section: Introductionmentioning

confidence: 99%

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

Sriram,

Ayena,

Ngongiah

et al. 2023

Phys. Scr.

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This paper evaluates the microcontroller implementation, offset boosting control, suppression of chaos, and combination of three types of synchronization in the autonomous piecewise damping Josephson junction (JJ) jerk oscillator (APDJJJO). The APDJJJO exhibits vast shapes of chaotic behaviors, bistable limit circles, bistable period-2-oscillation, and the coexistence of regular and chaotic behaviors exposed by numerical simulations. The microcontroller realization scheme of APDJJJO validates simulated dynamics. Proceeding, two constants are outlined in the rate equations of APDJJJO to achieve the linear offset boosting of constants based on the second and third state variables, respectively. The polarity of the chaotic signal of the second or third state variable can be flexibly altered by changing any of the two introduced constants while the other constant is kept at zero. When the two constants are equal, the second and third state variables can swap between bipolar and unipolar signals flexibly by altering the unique constant parameter. Moreover, theoretical probing is performed to validate the efficacy of the configured single controller engrossed in subduing chaos in APDJJJO. Lastly, the combination of three types of synchronization between two chaotic APDJJJO are analytically and numerically investigated.

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“…Regardless of whether it is a continuous chaotic system or a discrete iterative map, the nonlinear term plays an essential role in generating chaotic oscillation. Generally, these systems must have nonlinear terms, such as polynomials, absolute values, trigonometric functions [1][2][3][4][5]. The memristor, as an element with special nonlinearity, can induce complex dynamical behaviors [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Hyperchaotic maps of a discrete memristor coupled to trigonometric function

Liu¹,

Mou²,

Han³

et al. 2021

Phys. Scr.

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In this paper, a new chaotic map coupled with a memristor is constructed. Based on the proposed discrete maps of sine and cosine functions, the discrete memristor is introduced and used as input to enhance their chaotic performance. Then Lyapunov exponents spectra (LEs), bifurcation diagram, and other methods are used to evaluate their chaotic behaviors. Firstly, the fixed point of the new mapping is solved, and the stability of the fixed point is analyzed with different system parameters. The distinguishing feature of the discrete graph is the coexistence of multiple types such as chaos, quasiperiodic oscillation, and discrete periodic points. In particular, the coexistence of multiple chaotic and hyperchaotic attractors has been discovered, and the initial value can be adjusted to control the shift of the chaotic attractor. In addition, state transition phenomena such as chaos degeneration and the transformation of chaos into hyperchaos have been discovered. Finally, we designed and implemented the discrete map on the DSP platform. The research results provide guidance for the application and teaching of the chaotic map coupled discrete memristor.

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Hidden Attractors with Conditional Symmetry

Cited by 25 publications

References 45 publications

On Offset Boosting in Chaotic System

On Offset Boosting in Chaotic System

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

Hyperchaotic maps of a discrete memristor coupled to trigonometric function

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