Dynamical analysis of a simple autonomous jerk system with multiple attractors

Kengne, Jacques; Njitacke, Zeric Tabekoueng; Fotsin, Hilaire Bertrand

doi:10.1007/s11071-015-2364-y

Cited by 224 publications

(122 citation statements)

References 33 publications

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“…It is worth noting that the stability depends on the memristor initial condition in a memristive dynamical circuit, leading to the occurrence of coexisting multiple attractors [9,13]. The coexistence of different kinds of attractors, called multistability, reveals a rich diversity of stable states in nonlinear dynamical systems [12,[24][25][26][27][28][29][30][31][32] and makes the system offer great flexibility, which can be used for image processing or taken as an additional source of randomness used for many information engineering applications [32][33][34][35][36][37]. Therefore, it is very attractive to seek for a simple memristive chaotic circuit that has the striking dynamical behavior of coexisting multiple attractors.…”

Section: Introductionmentioning

confidence: 99%

An Improved Memristive Diode Bridge‐Based Band Pass Filter Chaotic Circuit

Zhang

Wang

et al. 2017

Mathematical Problems in Engineering

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By replacing a series resistor in active band pass filter (BPF) with an improved memristive diode bridge emulator, a third-order memristive BPF chaotic circuit is presented. The improved memristive diode bridge emulator without grounded limitation is equivalently achieved by a diode bridge cascaded with only one inductor, whose fingerprints of pinched hysteresis loop are examined by numerical simulations and hardware experiments. The memristive BPF chaotic circuit has only one zero unstable saddle point but causes complex dynamical behaviors including period, chaos, period doubling bifurcation, and coexisting bifurcation modes. Specially, it should be highly significant that two kinds of bifurcation routes are displayed under different initial conditions and the coexistence of three different topological attractors is found in a narrow parameter range. Moreover, hardware circuit using discrete components is fabricated and experimental measurements are performed, upon which the numerical simulations are validated. Notably, the proposed memristive BPF chaotic circuit is only third-order and has simple topological structure.

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Section: Introductionmentioning

confidence: 99%

An Improved Memristive Diode Bridge‐Based Band Pass Filter Chaotic Circuit

Zhang

Wang

et al. 2017

Mathematical Problems in Engineering

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“…It should be mentioned that just like the ideal flux/ voltage-controlled memristor-based chaotic circuits [4][5][6][7][8][9], the proposed memristor-based canonical Chua's circuit has a line equilibrium point with complicated stability distributions already depicted in Figures 2-4, whereas most of conventionally nonlinear dynamical systems with no equilibrium point [10], with only several determined equilibrium points [15][16][17][18][19][20][21], or with curves of equilibrium points [41][42][43] have relatively simple stability distributions with some divinable nonlinear dynamical behaviors.…”

Section: Coexisting Infinitely Many Attractors With Reference To Thementioning

confidence: 98%

“…Generally, multistability is confirmed in hardware experiments by randomly switching on and off experimental circuit supplies [9,[15][16][17][18][19][20][21] or by MATLAB numerical or PSPICE/PSIM circuit simulations [4][5][6][7][8][22][23][24][25][26][27][28]. Consequently, to direct the nonlinear dynamical circuit or system to a desired oscillating mode, an effective control approach should be proposed [12].…”

Section: Introductionmentioning

confidence: 99%

Memristor‐Based Canonical Chua’s Circuit: Extreme Multistability in Voltage‐Current Domain and Its Controllability in Flux‐Charge Domain

et al. 2018

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This paper investigates extreme multistability and its controllability for an ideal voltage-controlled memristor emulator-based canonical Chua's circuit. With the voltage-current model, the initial condition-dependent extreme multistability is explored through analyzing the stability distribution of line equilibrium point and then the coexisting infinitely many attractors are numerically uncovered in such a memristive circuit by the attraction basin and phase portraits. Furthermore, based on the accurate constitutive relation of the memristor emulator, a set of incremental flux-charge describing equations for the memristor-based canonical Chua's circuit are formulated and a dimensionality reduction model is thus established. As a result, the initial condition-dependent dynamics in the voltage-current domain is converted into the system parameter-associated dynamics in the flux-charge domain, which is confirmed by numerical simulations and circuit simulations. Therefore, a controllable strategy for extreme multistability can be expediently implemented, which is greatly significant for seeking chaos-based engineering applications of multistable memristive circuits.

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“…In that paper, they established a novel memristive hyperchaotic system with no equilibrium based on the newly proposed circuit realization scheme and investigated the phenomenon of extreme multistability with hidden oscillation that reveals the coexistence of infinitely many hidden attractors in the proposed memristive hyperchaotic system. Kengne et al [13] presented the basic dynamical properties of a simple autonomous jerk system including equilibria and stability, phase portraits, frequency spectra, bifurcation diagrams, and Lyapunov exponent plots. It is shown that the onset of chaos is achieved via the classical period-doubling and symmetryrestoring crisis scenarios.…”

Section: Complexitymentioning

confidence: 99%

Multistability Analysis and Function Projective Synchronization in Relay Coupled Oscillators

et al. 2018

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Regions of stability phases discovered in a general class of Genesio−Tesi chaotic oscillators are proposed. In a relatively large region of two-parameter space, the system has coexisting point attractors and limit cycles. The variation of two parameters is used to characterize the multistability by plotting the isospike diagrams for two nonsymmetric initial conditions. The parameters window in which the jerk system exhibits the unusual and striking feature of multiple attractors (e.g., coexistence of six disconnected periodic chaotic attractors and three-point attraction) is investigated. The second aspect of this study presents the synchronization of systems that act as mediators between two dynamical units that, in turn, show function projective synchronization (FPS) with each other. These are the so-called relay systems. In a wide range of operating parameters; this setup leads to synchronization between the outer circuits, while the relaying element remains unsynchronized. The results show that the coupled systems can achieve function projective synchronization in a determined time despite the unpredictability of the scaling function. In the coupling path, the outer dynamical systems show finite-time synchronization of their outputs, that is, displaying the same dynamics at exactly the same moment. Further, this effect is rather general and it has a wide range of applications where sustained oscillations should be retained for proper functioning of the systems.

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Dynamical analysis of a simple autonomous jerk system with multiple attractors

Cited by 224 publications

References 33 publications

An Improved Memristive Diode Bridge‐Based Band Pass Filter Chaotic Circuit

An Improved Memristive Diode Bridge‐Based Band Pass Filter Chaotic Circuit

Memristor‐Based Canonical Chua’s Circuit: Extreme Multistability in Voltage‐Current Domain and Its Controllability in Flux‐Charge Domain

Multistability Analysis and Function Projective Synchronization in Relay Coupled Oscillators

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