Coexisting infinitely many attractors in active band-pass filter-based memristive circuit

Bao, Bocheng; Jiang, Tao; Xu, Quan; Chen, Mo; Wu, Huagan; Hu, Yihua

doi:10.1007/s11071-016-2988-6

Cited by 198 publications

(73 citation statements)

References 44 publications

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“…The ideal voltage-controlled memristor emulator is equivalently implemented with an electronic circuit via op-amp integrators and analog multipliers [5,6,34], as shown in Figure 1(b). In our next work, the considered circuit parameters remained unchanged and are listed in Table 1, where is the total gain of two multipliers and .…”

Section: Extreme Multistability In the Voltage-current Domainmentioning

confidence: 99%

“…Similar to the memristive Chua's circuit containing an ideal voltagecontrolled memristor emulator [5,6], the memristor-based canonical Chua's circuit has a line equilibrium point, which is expressed by…”

Section: Stability Distribution Of Line Equilibriummentioning

confidence: 99%

“…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%

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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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Section: Extreme Multistability In the Voltage-current Domainmentioning

confidence: 99%

Section: Stability Distribution Of Line Equilibriummentioning

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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Harmonic balance method to analyze bifurcations in memristor oscillatory circuits

Marco

Forti

Innocenti

et al. 2017

Circuit Theory & Apps

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SUMMARYThe paper studies nonlinear dynamics and bifurcations of a class of memristor oscillatory circuits obtained by replacing the nonlinear resistor of a Chua's oscillator with a flux-controlled memristor. A recently developed technique, named flux-charge analysis method, has shown that the state space of such circuits can be decomposed in invariant manifolds, where each manifold is characterized by a different dynamics and different attractors. Goal of the paper is to investigate the use of the harmonic balance method in combination with flux-charge analysis method in order to study the different kinds of bifurcations generated by changing the circuit parameters on a fixed manifold, changing manifold for a fixed parameter set (bifurcations without parameters), or changing simultaneously circuit parameters and manifolds. The main result is that the harmonic balance method is quite simple to apply in this rich bifurcation context and is effective to detect Hopf and to accurately predict period-doubling bifurcations of all these different kinds.

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Coexisting infinitely many attractors in active band-pass filter-based memristive circuit

Cited by 198 publications

References 44 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

Harmonic balance method to analyze bifurcations in memristor oscillatory circuits

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