Self-Excited and Hidden Attractors Found Simultaneously in a Modified Chua's Circuit

2015 ◽  
Vol 25 (05) ◽  
pp. 1550075 ◽  
Author(s):  
Bocheng Bao ◽  
Fengwei Hu ◽  
Mo Chen ◽  
Quan Xu ◽  
Yajuan Yu
Keyword(s):  
Saddle Point ◽  
Fourth Order ◽  
Nonlinear Phenomena ◽  
Chua’S Circuit ◽  
Hidden Attractors ◽  
Parameter Region ◽  
Chua's Circuit ◽  
First Order ◽  
Dynamical Behaviors

By replacing the Chua's diode in Chua's circuit with a first-order hybrid diode circuit, a fourth-order modified Chua's circuit is presented. The circuit has an unstable zero saddle point and two nonzero saddle-foci. By Routh–Hurwitz criterion, it is found that in a narrow parameter region, the two nonzero saddle-foci have a transition from unstable to stable saddle-foci, leading to generations of self-excited and hidden attractors in the modified Chua's circuit simultaneously, which have not been previously reported. Complex dynamical behaviors are investigated both numerically and experimentally. The results indicate that the proposed circuit exhibits complicated nonlinear phenomena including self-excited attractors, coexisting self-excited attractors, hidden attractors, and coexisting hidden attractors.

Controlling Dynamics to Coexisting Periodic Solutions or Equilibrium Points of the n-Scroll Modified Chua’s Circuit

2019 ◽  
Vol 29 (13) ◽  
pp. 1950180 ◽  
Author(s):  
Shihui Fu ◽  
Ying Han ◽  
Huizhen Ma ◽  
Ying Du
Keyword(s):  
Periodic Solutions ◽  
Equilibrium Points ◽  
Linear Feedback ◽  
Chua’S Circuit ◽  
Control Parameters ◽  
Chua's Circuit ◽  
First Order ◽  
Dynamical Behaviors ◽  
Linear Feedback Controller ◽  
Boundary Equilibrium

The modified Chua’s circuit, which is first order differentiable, has degree-of-discontinuity [Formula: see text]. It has [Formula: see text] equilibrium points, including two boundary equilibrium points. For them, except boundary equilibrium points, we obtain in theory, conditions under which Hopf bifurcations exist, which implies coexisting periodic solutions. At the same time, we also show that equilibrium points are asymptotically stable when system parameters are within some limits. Furthermore, we theoretically design a linear feedback controller, which will not change the equilibrium points, with appropriate control parameters to control the dynamical behaviors including chaos to these periodic solutions or equilibrium points, and we verify it by numerical simulations.

Dynamics of self-excited attractors and hidden attractors in generalized memristor-based Chua’s circuit

2015 ◽  
Vol 81 (1-2) ◽  
pp. 215-226 ◽  
Author(s):  
Mo Chen ◽  
Mengyuan Li ◽  
Qing Yu ◽  
Bocheng Bao ◽  
Quan Xu ◽  
...  
Keyword(s):  
Chua’S Circuit ◽  
Hidden Attractors ◽  
Chua's Circuit

scholarly journals Colpitts Chaotic Oscillator Coupling with a Generalized Memristor

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Ling Lu ◽  
Changdi Li ◽  
Zicheng Zhao ◽  
Bocheng Bao ◽  
Quan Xu
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Fourth Order ◽  
Chaotic Attractors ◽  
Chaotic Oscillator ◽  
Nonlinear Phenomena ◽  
Unique Equilibrium ◽  
First Order ◽  
The Mathematical Model ◽  
Order Parallel

By introducing a generalized memristor into a fourth-order Colpitts chaotic oscillator, a new memristive Colpitts chaotic oscillator is proposed in this paper. The generalized memristor is equivalent to a diode bridge cascaded with a first-order parallel RC filter. Chaotic attractors of the oscillator are numerically revealed from the mathematical model and experimentally captured from the physical circuit. The dynamics of the memristive Colpitts chaotic oscillator is investigated both theoretically and numerically, from which it can be found that the oscillator has a unique equilibrium point and displays complex nonlinear phenomena.

scholarly journals Localization of Hidden Attractors in Chua’s System With Absolute Nonlinearity and Its FPGA Implementation

2021 ◽  
Vol 9 ◽  
Author(s):  
Xianming Wu ◽  
Huihai Wang ◽  
Shaobo He
Keyword(s):  
Basin Of Attraction ◽  
Digital Circuit ◽  
Fpga Implementation ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Hidden Attractor ◽  
Hidden Attractors ◽  
Chua's Circuit ◽  
The Mathematical Model ◽  
The Basin Of Attraction

Investigation of the classical self-excited and hidden attractors in the modified Chua’s circuit is a hot and interesting topic. In this article, a novel Chua’s circuit system with an absolute item is investigated. According to the mathematical model, dynamic characteristics are analyzed, including symmetry, equilibrium stability analysis, Hopf bifurcation analysis, Lyapunov exponents, bifurcation diagram, and the basin of attraction. The hidden attractors are located theoretically. Then, the coexistence of the hidden limit cycle and self-excited chaotic attractors are observed numerically and experimentally. The numerical simulation results are consistent with the FPGA implementation results. It shows that the hidden attractor can be localized in the digital circuit.

Hidden attractors and multistability in a modified Chua’s circuit

2021 ◽  
Vol 92 ◽  
pp. 105494
Author(s):  
Ning Wang ◽  
Guoshan Zhang ◽  
N.V. Kuznetsov ◽  
Han Bao
Keyword(s):  
Chua’S Circuit ◽  
Hidden Attractors ◽  
Chua's Circuit

scholarly journals Hidden Multistability in a Memristor-Based Cellular Neural Network

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Birong Xu ◽  
Hairong Lin ◽  
Guangyi Wang
Keyword(s):  
Neural Network ◽  
Simulation Analysis ◽  
Equilibrium Points ◽  
Cellular Neural Network ◽  
Nonlinear Phenomena ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Dynamical Behaviors ◽  
Circuit Simulations

In this paper, we report a novel memristor-based cellular neural network (CNN) without equilibrium points. Dynamical behaviors of the memristor-based CNN are investigated by simulation analysis. The results indicate that the system owns complicated nonlinear phenomena, such as hidden attractors, coexisting attractors, and initial boosting behaviors of position and amplitude. Furthermore, both heterogeneous multistability and homogenous multistability are found in the CNN. Finally, Multisim circuit simulations are performed to prove the chaotic characteristics and multistability of the system.

A New Fourth-Order Memristive Chaotic System and Its Generation

2015 ◽  
Vol 25 (11) ◽  
pp. 1550151 ◽  
Author(s):  
Yuxia Li ◽  
Xia Huang ◽  
Yiwen Song ◽  
Jinuan Lin
Keyword(s):  
Phase Diagram ◽  
Lyapunov Exponent ◽  
Chaotic System ◽  
Fourth Order ◽  
Bifurcation Analysis ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Diagram Analysis

In this paper, a new fourth-order memristive chaotic system is constructed on the basis of Chua's circuit. Chaotic behaviors are verified through a series of dynamical analyses, including Lyapunov exponent analysis, bifurcation analysis, and phase diagram analysis. In addition, chaos attractors in the newly-proposed system are implemented by hardware circuits.

HYPERCHAOS IN A CHUA'S CIRCUIT WITH TWO NEW ADDED BRANCHES

2008 ◽  
Vol 18 (04) ◽  
pp. 1151-1159 ◽  
Author(s):  
RUY BARBOZA
Keyword(s):  
Theoretical Analysis ◽  
Fourth Order ◽  
Current Source ◽  
Experimental Results ◽  
The Other ◽  
Chua’S Circuit ◽  
Series Connection ◽  
Chua's Circuit ◽  
Original Topology ◽  
Wide Range

In this work a fourth-order Chua's circuit, capable of generating hyperchaotic oscillations in a wide range of parameters, is presented. The circuit is obtained by adding two new branches to the original topology of the Chua's double scroll circuit. One of the added branches is a linear inductor-resistor series connection, and the other one is a nonlinear voltage-controlled current source. A theoretical analysis of the circuit equations is presented, along with numerical and experimental results.

TORUS BREAKDOWN TO CHAOS VIA PERIOD-3 DOUBLING ROUTE IN A MODIFIED CANONICAL CHUA'S CIRCUIT

2011 ◽  
Vol 21 (07) ◽  
pp. 1987-1998 ◽  
Author(s):  
I. MANIMEHAN ◽  
K. THAMILMARAN ◽  
P. PHILOMINATHAN
Keyword(s):  
Autonomous System ◽  
Chua’S Circuit ◽  
System Behavior ◽  
Chua's Circuit ◽  
Pspice Simulations ◽  
Numerical Studies ◽  
Dynamical Behaviors ◽  
Torus Breakdown ◽  
Canonical Chua’S Circuit

In this paper, we report the dynamical behaviors of a four-dimensional autonomous system, that is, the modified canonical Chua's circuit. An interesting transition of three-tori–period-3 doubling–chaos is observed when the circuit parameters are varied in the range of our choice. Furthermore, the detailed numerical studies of the system behavior with supporting PSPICE simulations and hardware experiments are also presented here.

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