Coexistence of multiple attractors and crisis route to chaos in a novel memristive diode bidge-based Jerk circuit

Njitacke, Zeric Tabekoueng; Kengne, Jacques; Fotsin, Hilaire Bertrand; Negou, A. Nguomkam; Tchiotsop, Daniel

doi:10.1016/j.chaos.2016.05.011

Cited by 147 publications

(52 citation statements)

References 38 publications

(47 reference statements)

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“…Due to the unique nonlinear characteristics of memristors [1], an explosive growth study of memristor based circuits has been boosted up in the past years [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Unfortunately, induced by technical handicaps in fabricating nanoscale memristor, the commercial memristor is not expected to be available in the near future.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, various kinds of physically implementable equivalent circuits which can manifest the three fingerprints of memristors [17] have attracted much attention [2,[6][7][8][9][10][11][12][13][14][15][16][17][18]. Popularly, the circuits implemented by operational amplifiers and analog multipliers [7][8][9][10][11][12] as well as the circuits consisting of diode bridge cascaded with RC [13][14][15], LC [16], and RLC [18] filters have been used for experimental measurements in memristor based circuits. The most significant feature of the memristive diode bridge emulators is ungrounded limitation, which makes it as a serial expandable and flexible element in designing memristor based circuit [19].…”

Section: Introductionmentioning

confidence: 99%

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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%

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: 99%

“…Based on (15)- (20), it can be known that the line equilibrium point described by (6) in the voltage-current domain is converted into several determined equilibrium points represented by (15) in the flux-charge domain, whose locations and stabilities are decided by the initial conditionrelated system parameters , 1 , 2 , and 3 . Therefore, the extreme multistability in the voltage-current domain can readily be controlled by the system parameters in the fluxcharge domain.…”

Section: System Parameter-related Stability Distributionmentioning

confidence: 99%

“…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%

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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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Crisis‐induced coexisting multiple attractors in a second‐order nonautonomous memristive diode bridge‐based circuit

Zhang

Qian

et al. 2018

Circuit Theory & Apps

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SummaryThis paper reports a second‐order nonautonomous memristive diode bridge‐based circuit, upon which a system model is established. The AC and DC equilibrium points and their stability evolutions are theoretically analyzed, and the mechanisms of complex dynamical behaviors are explored in detail. Furthermore, the stimulus‐dependent dynamical behaviors are numerically performed by the single‐parameter bifurcation diagrams, Lyapunov exponents, and phase portraits. Of particular concern, it should be highly emphasized that multiple kinds of crisis scenarios associated with the initial conditions are found in a specified parameter region, resulting in that coexisting multiple attractors under different initial conditions are discovered for the fixed system parameters. Additionally, hardware experiments and PSpice circuit simulations are used to confirm the numerically simulated results.

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Coexistence of multiple attractors and crisis route to chaos in a novel memristive diode bidge-based Jerk circuit

Cited by 147 publications

References 38 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

Crisis‐induced coexisting multiple attractors in a second‐order nonautonomous memristive diode bridge‐based circuit

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