Two-memristor-based Chua’s hyperchaotic circuit with plane equilibrium and its extreme multistability

Bao, Bocheng; Jiang, Tao; Wang, Guangyi; Jin, Peipei; Bao, Han; Chen, Mo

doi:10.1007/s11071-017-3507-0

Cited by 226 publications

(102 citation statements)

References 35 publications

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“…Due to the existence of the zero eigenvalue, the stability of the memristor-based canonical Chua's circuit can not be simply determined by the three nonzero eigenvalues of the line equilibrium point. The following numerical simulations demonstrate that the zero eigenvalue also has influence on the dynamics of the circuit under some circuit parameters [6][7][8][9].…”

Section: Stability Distribution Of Line Equilibriummentioning

confidence: 92%

“…More recently, due to the existence of infinitely many equilibrium points, for example, line equilibrium point or plane equilibrium point, this special dynamical phenomenon of extreme multistability is naturally exhibited in a class of ideal flux/voltage-controlled memristor-based chaotic circuits/systems [4][5][6][7][8][9], thereby leading to the emergence of infinitely many disconnected attractors.…”

Section: Introductionmentioning

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%

“…Besides, for a memristor-based circuit or system with line equilibrium point or plane equilibrium point, its stability at the equilibrium point is very difficult to be determined due to the existence of one or two zero eigenvalues [5][6][7][8][9], which results in the fact that the coexisting infinitely many attractors' behaviors can not be precisely interpreted from the stabilities of the nonzero eigenvalues. As a matter of fact, the memristor initial condition and other initial conditions all have dynamical effects on the memristor-based circuit or system [8,9].…”

Section: Introductionmentioning

confidence: 99%

“…As a matter of fact, the memristor initial condition and other initial conditions all have dynamical effects on the memristor-based circuit or system [8,9]. However, the dynamical effects are implied, which can not be explicitly expressed in the voltage-current domain.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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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Section: Stability Distribution Of Line Equilibriummentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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Coexisting attractors in a fractional order hydro turbine governing system and fuzzy PID based chaos control

Rajagopal

Jahanshahi

Jafari

et al. 2020

Asian Journal of Control

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A fractional order model of a hydro turbine governing system (FOHTGS) is derived using the Grunwald‐Letnikov's (GL) method. This model is developed using its integer order. Dynamical properties of FOHTGS, such as equilibrium point and its stability, Hopf bifurcation, and Lyapunov exponents (LEs) are investigated. Different dynamics of FOHTGS with respect to changing fractional order of the system and its parameter are studied. The FOHTGS shows multistability and coexisting attractors. To support the existence of multistability, some coexisting attractors are presented. A fuzzy PID based chaos control algorithm is designed and proposed in a hydro turbine governing system (HTGS). Numerical simulations are conducted to validate the effectiveness of the derived controller.

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Dynamic analysis and chaos control of the switched‐inductor boost converter with the memristive load

Zhang

Yang

Wang

2021

Circuit Theory & Apps

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SummaryThis paper investigates dynamic behaviors and the time‐delay feedback control method for a peak current mode (PCM) controlled switched‐inductor boost converter with a memristive load. The research contents include the following: (1) The state equations are constructed for the PCM switched‐inductor boost converter with the memristive load. (2) The bifurcation and chaos behaviors of the boost converter are analyzed by the MATLAB numerical simulation. (3) The Power Simulation (PSIM) circuit simulation of the switched‐inductor boost converter is illustrated the correctness of the MATLAB numerical simulation. (4) The time‐delay feedback control is adopted to suppress the bifurcation and chaos behaviors of the boost converter and is verified being effective.

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Two-memristor-based Chua’s hyperchaotic circuit with plane equilibrium and its extreme multistability

Cited by 226 publications

References 35 publications

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

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

Coexisting attractors in a fractional order hydro turbine governing system and fuzzy PID based chaos control

Dynamic analysis and chaos control of the switched‐inductor boost converter with the memristive load

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