Effects of symmetric and asymmetric nonlinearity on the dynamics of a novel chaotic jerk circuit: Coexisting multiple attractors, period doubling reversals, crisis, and offset boosting

Kengne, Jacques; Mogue, R. L. Tagne; Fozin, T. Fonzin; Telem, Adélaïde Nicole Kengnou

doi:10.1016/j.chaos.2019.01.033

Cited by 54 publications

(14 citation statements)

References 59 publications

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“…If not, the stable states produced will remain symmetric if the real symmetry of the attractors has already been re-established. is approach has been widely exploited recently to find coexisting attractors in symmetrical systems such as jerk [6,8,[52][53][54][55][56], hyperchaotic and chaotic Chua's oscillators [3,44,[57][58][59], Hopfield neural networks [10,36,60,61], and Duffing oscillator [9], just to name a few. In addition, it is easy to show that the model processes three equilibrium points given by the following expression: S 0 � 0 0 0 , and S…”

Section: Description Of Chua's Oscillator With Smooth Nonlinearitymentioning

confidence: 99%

“…In the study of nonlinear dynamic systems, the simultaneous existence of attractors (finite or infinite), also known as multistability [1][2][3][4][5][6][7][8][9][10][11][12][13], extreme multistability [14][15][16], or megastability [17], is now in the forefront. Recall that the famous Chua's circuit is among the widely studied electronic circuits capable to display chaos [18].…”

Section: Introductionmentioning

confidence: 99%

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Control of Coexisting Attractors with Preselection of the Survived Attractor in Multistable Chua’s System: A Case Study

Njitacke

Fozin²,

Tchapga

et al. 2020

Complexity

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Although the control of multistability has already been reported, the one with preselection of the desired attractor is still uncovered in systems with more than two coexisting attractors. This work reports the control of coexisting attractors with preselection of the survived attractors in paradigmatic Chua’s system with smooth cubic nonlinearity. Techniques of linear augmentation combined to system invariant parameters like equilibrium points are used to choose the desired surviving attractors among the coexisting ones. Nonlinear dynamical tools including bifurcation diagrams, standard Lyapunov exponents, phase portraits, and cross section of initial conditions are exploited to reveal the selection scenarios of the survived attractor in the multistability control process of Chua’s system. The main crisis towards annihilation of multistability in Chua’s system when varying the coupling strength is interior crisis and border collision. Theoretical and numerical results obtained are further validated with PSpice analysis.

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Section: Description Of Chua's Oscillator With Smooth Nonlinearitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Control of Coexisting Attractors with Preselection of the Survived Attractor in Multistable Chua’s System: A Case Study

Njitacke

Fozin²,

Tchapga

et al. 2020

Complexity

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“…However, the physical memristor device usually possesses the asymmetric hysteresis loops [2], [22]. The influence of symmetric-breaking phenomenon on the dynamical systems has attracted much attention [23]- [27]. Recently, Kengne et al took the antiparallel semiconductor diodes pair as an asymmetric nonlinear emulator, upon which various asymmetry-induced dynamical behaviors were revealed in several asymmetric chaotic circuits [28]- [31].…”

Section: Introductionmentioning

confidence: 99%

Parallel-Type Asymmetric Memristive Diode-Bridge Emulator and Its Induced Asymmetric Attractor

Zhou

et al. 2020

IEEE Access

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Symmetry brings beauty, while asymmetry is the general law of nature. This paper reports a novel parallel-type asymmetric memristive diode-bridge (AMDB) emulator, which is implemented by an unbalance diode-bridge linked with a RC filter. Following the voltage constraints of the unbalance diodebridge, the mathematical model of the parallel-type AMDB emulator is established. Thereafter, the asymmetric property of the hysteresis loops is demonstrated by the numerical simulations and confirmed by the hardware experiments. Furthermore, by importing the parallel-type AMDB emulator into the classical Chua's circuit, a novel memristive Chua's circuit is proposed, so that the asymmetric double-scroll chaotic attractor, asymmetric coexisting single-scroll chaotic attractors, and asymmetric coexisting limit cycles can be revealed herein. The parallel-type AMDB emulator enriches the types of memristor emulators and it can mimic the asymmetric property of the physical memristor device.

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“…e authors of [39][40][41] did similar works by considering adjustable symmetry and nonlinearities in the dynamics of a simple jerk system, snap system, and jerk circuit, respectively. As far as symmetry breaking is concerned, the results obtained highlighted issues, such as the presence of parallel bifurcation branches, hysteresis, and coexisting multiple asymmetric attractors in the mentioned systems and circuits.…”

Section: Introductionmentioning

confidence: 99%

Effects of Symmetric and Asymmetric Nonlinearity on the Dynamics of a Third-Order Autonomous Duffing–Holmes Oscillator

et al. 2020

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A generalized third-order autonomous Duffing–Holmes system is proposed and deeply investigated. The proposed system is obtained by adding a parametric quadratic term m x 2 to the cubic nonlinear term − x 3 of an existing third-order autonomous Duffing–Holmes system. This modification allows the system to feature smoothly adjustable nonlinearity, symmetry, and nontrivial equilibria. A particular attention is given to the effects of symmetric and asymmetric nonlinearity on the dynamics of the system. For the specific case of m = 0 , the system is symmetric and interesting phenomena are observed, namely, coexistence of symmetric bifurcations, presence of parallel branches, and the coexistence of four (periodic-chaotic) and six (periodic) symmetric attractors. For m ≠ 0 , the system loses its symmetry. This favors the emergence of other behaviors, such as the coexistence of asymmetric bifurcations, involving the coexistence of several asymmetric attractors (periodic-periodic or periodic-chaotic). All these phenomena have been numerically highlighted using nonlinear dynamic tools (bifurcation diagrams, Lyapunov exponents, phase portraits, time series, frequency spectra, Poincaré section, cross sections of the attraction basins, etc.) and an analog computer of the system. In fact, PSpice simulations of the latter confirm numerical results. Moreover, amplitude control and synchronization strategies are also provided in order to promote the exploitation of the proposed system in engineering.

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Effects of symmetric and asymmetric nonlinearity on the dynamics of a novel chaotic jerk circuit: Coexisting multiple attractors, period doubling reversals, crisis, and offset boosting

Cited by 54 publications

References 59 publications

Control of Coexisting Attractors with Preselection of the Survived Attractor in Multistable Chua’s System: A Case Study

Control of Coexisting Attractors with Preselection of the Survived Attractor in Multistable Chua’s System: A Case Study

Parallel-Type Asymmetric Memristive Diode-Bridge Emulator and Its Induced Asymmetric Attractor

Effects of Symmetric and Asymmetric Nonlinearity on the Dynamics of a Third-Order Autonomous Duffing–Holmes Oscillator

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