Memristive oscillator based on Chua’s circuit: stability analysis and hidden dynamics

Rocha, Ronilson; Ruthiramoorthy, Jothimurugan; Thamilmaran, K.

doi:10.1007/s11071-017-3396-2

Cited by 34 publications

(14 citation statements)

References 37 publications

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“…where v c1 and v c2 are the voltages of C 1 and C 2 , respectively; i l is the current of L; and f(v c1 ) is the volt-ampere characteristic function of a nonlinear resistor. e excitation current [15,16] is denoted by i s F sin(Ωt + Φ) in which F, Ω, and Φ represent the amplitude, frequency, and initial phase of the excitation current, respectively. By the coordinate and dimensionless transformation,…”

Section: Mathematical Modelmentioning

confidence: 99%

Attractor and Vector Structure Analyses of Bursting Oscillation with Sliding Bifurcation in Filippov Systems

2019

Shock and Vibration

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The main purpose of this paper is to investigate the mechanism of sliding phenomenon in Filippov (nonsmooth) dynamical systems by attractor analysis and vector analysis. A corresponding simple model based on Chua’s circuit with periodic excitation was introduced as an example. The attractor analysis proposed in our previous work is used to discuss the complicated oscillations of the Filippov system. However, it failed to perfectly explain the sliding phenomena and establish an analytical method of constant voltage control. Therefore, the geometric structure and analytic conditions of sliding bifurcations in the general n-dimensional piecewise smooth system are discussed in detail by vector structure analysis. The prospects of practical application of this method are also discussed in the end.

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Section: Mathematical Modelmentioning

confidence: 99%

Attractor and Vector Structure Analyses of Bursting Oscillation with Sliding Bifurcation in Filippov Systems

2019

Shock and Vibration

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“…Further study of the hidden Chua attractors and their observation in physical experiments can be found, e.g. in Chen et al, 2015a;Bao et al, 2015a;Chen et al, 2015c,b;Zelinka, 2016;Bao et al, 2016;Menacer et al, 2016;Chen et al, 2017a;Rocha et al, 2017;Hlavacka & Guzan, 2017]. The synchronization of Chua circuits with hidden attractors is discussed, e.g.…”

Section: Introductionmentioning

confidence: 96%

Scenario of the Birth of Hidden Attractors in the Chua Circuit

Stankevich

Kuznetsov

Леонов

et al. 2017

Int. J. Bifurcation Chaos

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Recently it was shown that in the dynamical model of Chua circuit both the classical selfexcited and hidden chaotic attractors can be found. In this paper the dynamics of the Chua circuit is revisited. The scenario of the chaotic dynamics development and the birth of selfexcited and hidden attractors is studied. It is shown a pitchfork bifurcation in which a pair of symmetric attractors coexists and merges into one symmetric attractor through an attractormerging bifurcation and a splitting of a single attractor into two attractors. The scenario relating the subcritical Hopf bifurcation near equilibrium points and the birth of hidden attractors is discussed.Comment: 20 pages, 11 figure

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“…The nonlinear current-voltage characteristic i D (v 1 ) of the Chua diode is usually a three-segmented piecewise linear function (Chua et al, 1987;Brown, 1993;Tsuneda, 2005;Rocha and Medrano-T., 2009). Other nonlinearities have been proposed for Chua diode, such as cubic polynomial functions and "cubic-like" approximations (Zhong, 1994;Eltawil and Elwakil, 1999;O'Donoghue et al, 2005;Tsuneda, 2005;Rocha and Medrano-T., 2020), sigmoid and signum functions (Brown, 1993), odd square law ax + bx|x| (Tang and Man, 1998), trigonometric functions (Tang et al, 2001), memristive current-voltage characteristics (Rocha et al, 2017), etc. In despite of its simplicity, the Chua circuit generates a great diversity of nonlinear phenomena such as fixed and equilibrium points, periodic and stranger attractors, Andronov-Hopf, saddle-node (tangent), flip (period-doubling), cusp, homoclinic, heteroclinic, and other kinds of bifurcations, multistability and hidden oscillations, antiperiodic oscillations, period-adding in sets of periodicity, metamorphoses of basins of attraction, etc (Madan, 1993;Medrano-T. et al, 2005;Algaba et al, 2012;Leonov and Kuznetsov, 2013;Medrano-T. and Rocha, 2014;Singla et al, 2015;Menacer et al, 2016;Bao et al, 2016Bao et al, , 2018Singla et al, 2018;Liu et al, 2020;Wang et al, 2021).…”

Section: Introductionmentioning

confidence: 99%

Chua Circuit based on the Exponential Characteristics of Semiconductor Devices

Rocha,

Medrano-T

2021

Preprint

Self Cite

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The use of non-ideal features of semiconductor devices is an interesting option for implementations of nonlinear electronic systems. This paper analyzes the Chua circuit with nonlinearity based on the exponential hyperbolic characteristics of semiconductor devices. The stability analysis using describing functions predicts the dynamics of this nonlinear system, which is corroborated by numerical investigations and experimental results. The dynamic behaviors and bifurcations of this nonlinear system are mapped in parameter space in order to create a base for studies, analyses, and designs. The dynamic behavior of the experimental high speed implementation of this version of Chua circuit differs from the expected dynamics for a conventional Chua circuit due to effects of unmodelled non-idealities of the real semiconductor devices,displaying that new and different dynamics for the Chua circuit can be obtained exploring different nonlinearities.

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Memristive oscillator based on Chua’s circuit: stability analysis and hidden dynamics

Cited by 34 publications

References 37 publications

Attractor and Vector Structure Analyses of Bursting Oscillation with Sliding Bifurcation in Filippov Systems

Attractor and Vector Structure Analyses of Bursting Oscillation with Sliding Bifurcation in Filippov Systems

Scenario of the Birth of Hidden Attractors in the Chua Circuit

Chua Circuit based on the Exponential Characteristics of Semiconductor Devices

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