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

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Han Bao ◽  
Tao Jiang ◽  
Kaibin Chu ◽  
Mo Chen ◽  
Quan Xu ◽  
...  
Keyword(s):  
Current Model ◽  
Phase Portraits ◽  
Initial Condition ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Attraction Basin ◽  
Extreme Multistability ◽  
Canonical Chua’S Circuit ◽  
Flux Charge ◽  
Memristor Emulator

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.

Flux-Charge Analysis of Initial State-Dependent Dynamical Behaviors of a Memristor Emulator-Based Chua’s Circuit

2018 ◽  
Vol 28 (10) ◽  
pp. 1850120 ◽  
Author(s):  
Mo Chen ◽  
Bocheng Bao ◽  
Tao Jiang ◽  
Han Bao ◽  
Quan Xu ◽  
...  
Keyword(s):  
Equilibrium Points ◽  
Chua’S Circuit ◽  
Initial State ◽  
Chua's Circuit ◽  
Dynamical Behaviors ◽  
State Dependent ◽  
Initial States ◽  
Original Line ◽  
Flux Charge ◽  
Memristor Emulator

It is known that dynamical behaviors of memristive circuit are significantly affected by its initial states, which are difficult to be explicitly analyzed or controlled in voltage–current domain and have become great obstacles for its potential engineering applications. In this paper, the complex initial state-dependent dynamical behaviors of a physically realized memristive Chua’s circuit are detailed and investigated using incremental flux-charge modeling method. This circuit is modeled in terms of incremental flux and charge, in which the original line equilibrium point is converted into some determined equilibrium points relying on the initial states of the dynamic elements. Moreover, the special initial state-dependent behaviors are transformed into system parameter-associated behaviors. Consequently, the detailed influences of each initial state, even the occurrence of hidden oscillations, can readily be theoretically interpreted. Finally, the initial state-dependent behaviors are physically captured and directed in the equivalent realization circuit of the incremental flux-charge model.

HYPERCHAOS IN A MEMRISTOR-BASED MODIFIED CANONICAL CHUA'S CIRCUIT

2012 ◽  
Vol 22 (06) ◽  
pp. 1250133 ◽  
Author(s):  
ANDREW L. FITCH ◽  
DONGSHENG YU ◽  
HERBERT H. C. IU ◽  
VICTOR SREERAM
Keyword(s):  
Solid State ◽  
Lyapunov Exponents ◽  
Systematic Study ◽  
Phase Portraits ◽  
Chua’S Circuit ◽  
Bifurcation Diagrams ◽  
Nonlinear Characteristics ◽  
Chua's Circuit ◽  
Canonical Chua’S Circuit

After the successful solid state implementation of the memristor, memristor-based circuits have received a lot of attention. In this paper, a memristor with cubic nonlinear characteristics is employed in the modified canonical Chua's circuit. A systematic study of hyperchaotic behavior in this circuit is performed with the help of nonlinear tools such as Lyapunov exponents, phase portraits and bifurcation diagrams. In particular, an imitative memristor circuit is examined to reveal the construction of hyperchaotic attractors.

Controlling extreme multistability of memristor emulator-based dynamical circuit in flux–charge domain

2017 ◽  
Vol 91 (2) ◽  
pp. 1395-1412 ◽  
Author(s):  
Mo Chen ◽  
Mengxia Sun ◽  
Bocheng Bao ◽  
Huagan Wu ◽  
Quan Xu ◽  
...  
Keyword(s):  
Extreme Multistability ◽  
Flux Charge ◽  
Memristor Emulator

CHARACTERISATION OF CHAOS IN CHUA'S OSCILLATOR IN TERMS OF UNSTABLE PERIODIC ORBITS

1993 ◽  
Vol 03 (02) ◽  
pp. 411-429 ◽  
Author(s):  
MACIEJ J. OGORZAŁEK ◽  
ZBIGNIEW GALIAS
Keyword(s):  
Periodic Orbits ◽  
Picture Book ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Unstable Periodic Orbits ◽  
Chua's Circuit ◽  
Chua’S Oscillator ◽  
Canonical Chua’S Circuit

We present a picture book of unstable periodic orbits embedded in typical chaotic attractors found in the canonical Chua's circuit. These include spiral Chua's, double-scroll Chua's and double hook attractors. The "skeleton" of unstable periodic orbits is specific for the considered attractor and provides an invariant characterisation of its geometry.

Coexistence of multiple bifurcation modes in memristive diode-bridge-based canonical Chua’s circuit

2018 ◽  
Vol 105 (7) ◽  
pp. 1159-1169 ◽  
Author(s):  
Bocheng Bao ◽  
Li Xu ◽  
Zhimin Wu ◽  
Mo Chen ◽  
Huagan Wu
Keyword(s):  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Canonical Chua’S Circuit
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