Interpreting initial offset boosting via reconstitution in integral domain

Chen, Mo; Ren, Xue; Wu, Huagan; Xu, Quan; Bao, Bocheng

doi:10.1016/j.chaos.2019.109544

Cited by 41 publications

(8 citation statements)

References 45 publications

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“…Although some research articles have been published in recent years on the implementation of multi-stability, these methods are only suitable for continuous chaotic systems. Therefore, it is necessary to study the coexistence of stable attractors in discrete chaotic maps [31]. However, this discrete-time chaotic map is rarely reported in the existing literature.…”

Section: Two-variable Boosting Bifurcation In a Hyperchaotic Map And ...mentioning

confidence: 99%

Two-variable boosting bifurcation in a hyperchaotic map and its hardware implementation

Wang

Zhang

et al. 2022

Nonlinear Dyn

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There are few reports on the nondestructive adjustment of the oscillation amplitude of the chaotic sequence in the discrete map. To study the lossless regulation of the oscillation amplitude of chaotic sequences, this article proposes a new simple two-dimensional (2D) hyperchaotic map with trigonometric functions. It not only exhibits contains the offset boosting bifurcation and offset boosting coexistence attractors, but also realizes the offset boosting of two state variables with respect to arbitrary parameters in the 2D map. The simulation results of bifurcation diagram, maximum Lyapunov exponent and attractor phase diagram show that the map can produce complex dynamical behaviors. In addition, the introduction of new control parameters into the 2D hyperchaotic chaotic map can also make the hyperchaotic map exhibit rich multistable phenomena. At the same time, the common change of the initial state and the control parameters can realize the arbitrary switching and co-existence of the attractor in the phase plane. In the end, the 2D hyperchaotic map was tested and verified by hardware experiment platform.

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Section: Two-variable Boosting Bifurcation In a Hyperchaotic Map And ...mentioning

confidence: 99%

Two-variable boosting bifurcation in a hyperchaotic map and its hardware implementation

Wang

Zhang

et al. 2022

Nonlinear Dyn

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“…Later, based on the theory, the first entity of TiO2 memristor was developed by HP laboratory, and it is becoming more and more interesting in lots of engineering areas such as non-volatile memories, nonlinear circuit designs, and so on [2][3][4]. So far, the characteristics of memristor have been explored extensively, such as input frequency, input amplitude and initial value-dependent dynamics behaviors [5,6], and the local activity was considered as the origin of complexity [7]. In 2014, the first locally active memristor was proposed and verified physically by Chua [8].…”

Section: Introductionmentioning

confidence: 99%

A new locally active memristive synapse-coupled neuron model

Wang

Dong

2021

Nonlinear Dyn

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In this paper, a new type of non-volatile locally active memristor with bi-stability is proposed by injecting appropriate voltage pulses to realize a switching mechanism between two stable states. It is found that the memristive parameters of the new memristor can affect the local activity, which has been rarely reported, and this phenomenon is explained based on mathematical analyses and numerical simulations. Then, a locally active memristive coupled neuron model is constructed using the proposed memristor as a connecting synapse. The parameter-associated dynamical behaviors are revealed by bifurcation plots, phase plane portraits and dynamical evolution maps. Moreover, the bi-stability phenomenon of the new coupled neuron model is disclosed by local attraction basins, and the periodic burster and multi-scroll chaotic burster are found if a multi-level pulse current is used to imitate a periodical external stimulus on the neurons. The Hamiltonian energy function is calculated and analyzed with or without external excitation. Finally, the neuronal circuit is designed and implemented, which can mimic electrical activity of the neurons and is useful for physical applications. The experimental results captured from the

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“…Any chaotic signal has its inherent features namely identified as scale (C. Sprott and Xiong 2015;C. Sprott 2010;Gu et al 2021;Lu et al 2019;Liu et al 2020;Wang et al 2020;Zhao et al 2020;Akgul et al 2016Akgul et al , 2019Falco et al 2012) and offset (Li et al 2019(Li et al , 2017aLiu et al 2020;Li and Sprott 2017;Li et al 2021Li et al , 2017bKingni et al 2020;Ma et al 2021;Zhang et al 2018;Mezatio et al 2019;Bao et al 2020;Chen et al 2020;Zhang et al 2020;Wu et al 2019a;Ding et al 2020). For rescaling a chaotic signal, people usually design dynamical systems with amplitude control from the very beginning.…”

Section: Introductionmentioning

confidence: 99%

“…For this reason, offset boosting has attracted great interests recently both in continuous system and in discrete maps. Researchers pays great effort to learn how to get those attractors controlled by parameters (Li et al 2017b;Kingni et al 2020;Ma et al 2021;Zhang et al 2018;Mezatio et al 2019) or by initial conditions (Bao et al 2020;Chen et al 2020;Zhang et al 2020;Wu et al 2019a;Ding et al 2020). Even in those memristive systems (Chen et al 2019;Kengne et al 2018;Lu et al 2020;Wu et al 2019b;Yuan et al 2019) offset boosting is still a hot spot for discussion.…”

Section: Introductionmentioning

confidence: 99%

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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Interpreting initial offset boosting via reconstitution in integral domain

Cited by 41 publications

References 45 publications

Two-variable boosting bifurcation in a hyperchaotic map and its hardware implementation

Two-variable boosting bifurcation in a hyperchaotic map and its hardware implementation

A new locally active memristive synapse-coupled neuron model

On Offset Boosting in Chaotic System

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