Simple Double-Scroll Chaotic Circuit Based on Meminductor

2019 ◽  
Vol 29 (03) ◽  
pp. 2050048
Author(s):  
D. D. Zhai ◽  
F. Q. Wang
Keyword(s):  
Theoretical Analysis ◽  
Chaotic Attractors ◽  
Hidden Attractors ◽  
Chaotic Circuit ◽  
Initial Value ◽  
Memory Element ◽  
Dynamical Behaviors ◽  
Pinched Hysteresis Loop ◽  
Hardware Circuit ◽  
Pinched Hysteresis

Meminductor has attracted more and more attention as the new memory element. In this paper, a new generic meminductor model is proposed and analyzed. Its emulator is designed and its pinched hysteresis loop is presented. Based on the established meminductor and using a traditional capacitor and resistor, a new simple chaotic circuit presenting double-scroll chaotic attractors is proposed and its dynamical behaviors including phase portrait, Lyapunov exponents, Poincare mapping, power spectrum, bifurcation and the sensibility of initial value are analyzed. Meanwhile, it has been found that hidden attractors and transient chaotic phenomena under different initial value. Finally, the hardware circuit for the proposed simple double-scroll chaotic system is constructed and some experimental results are presented for validating the correctness of the theoretical analysis.

A New Simple Chaotic Circuit Based on Memristor

2016 ◽  
Vol 26 (09) ◽  
pp. 1650145 ◽  
Author(s):  
Renping Wu ◽  
Chunhua Wang
Keyword(s):  
Chaotic System ◽  
Electronic Circuit ◽  
Low Cost ◽  
Phase Portraits ◽  
Periodic Excitation ◽  
Simple Circuit ◽  
Chaotic Circuit ◽  
Dynamical Behaviors ◽  
Pinched Hysteresis Loop ◽  
Pinched Hysteresis

In this paper, a new memristor is proposed, and then an emulator built from off-the-shelf solid state components imitating the behavior of the proposed memristor is presented. Multisim simulation and breadboard experiment are done on the emulator, exhibiting a pinched hysteresis loop in the voltage–current plane when the emulator is driven by a periodic excitation voltage. In addition, a new simple chaotic circuit is designed by using the proposed memristor and other circuit elements. It is exciting that this circuit with only a linear negative resistor, a capacitor, an inductor and a memristor can generate a chaotic attractor. The dynamical behaviors of the proposed chaotic system are analyzed by Lyapunov exponents, phase portraits and bifurcation diagrams. Finally, an electronic circuit is designed to implement the chaotic system. For the sake of simple circuit topology, the proposed chaotic circuit can be easily manufactured at low cost.

The Design and Realization of a Hyper-Chaotic Circuit Based on a Flux-Controlled Memristor with Linear Memductance

2017 ◽  
Vol 27 (03) ◽  
pp. 1850038 ◽  
Author(s):  
Chunhua Wang ◽  
Ling Zhou ◽  
Renping Wu
Keyword(s):  
Chaotic System ◽  
Circuit Simulation ◽  
Piecewise Linear ◽  
Chaotic Circuit ◽  
Multiple Attractors ◽  
Dynamical Behaviors ◽  
Memristive System ◽  
Pinched Hysteresis Loop ◽  
The Lorenz System ◽  
Pinched Hysteresis

In this paper, a flux-controlled memristor with linear memductance is proposed. Compared with the memristor with piecewise linear memductance and the memristor with smooth continuous nonlinearity memductance which are widely used in the study of memristive chaotic system, the proposed memristor has simple mathematical model and is easy to implement. Multisim circuit simulation and breadboard experiment are realized, and the memristor can exhibit a pinched hysteresis loop in the voltage–current plane when driven by a periodic voltage. In addition, a new hyper-chaotic system is presented in this paper by adding the proposed memristor into the Lorenz system. The transient chaos and multiple attractors are observed in this memristive system. The dynamical behaviors of the proposed system are analyzed by equilibria, Lyapunov exponents, bifurcation diagram and phase portrait. Finally, an electronic circuit is designed to implement the hyper-chaotic memristive system.

scholarly journals Controlling Hyper Chaos with Feedback of Dynamical Variables

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4272-4277 ◽  
Author(s):  
Xiao-Shu Luo ◽  
Bing-Hong Wang
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Theoretical Analysis ◽  
Chaotic Attractors ◽  
Chaotic Circuit ◽  
Controlled System ◽  
Controlling Chaos ◽  
Simulation Results ◽  
System Variables ◽  
Proportional Feedback

We propose a method for controlling chaos and hyper-chaos by applying continuous proportional feedback to the system variables and their derivatives. The method has been applied successfully in six-order coupled Chua's hyper-chaotic circuit system. The theoretical analysis and numerical simulation results show that unstable fixed points embedded in hyper-chaotic attractors can be stabilized and Hopf bifurcation can be observed for the controlled system.

scholarly journals A Meminductor-based Chaotic System

2020 ◽  
Vol 49 (2) ◽  
pp. 317-332
Author(s):  
Aixue Qi ◽  
Lei Ding ◽  
Wenbo Liu
Keyword(s):  
Theoretical Analysis ◽  
Chaotic System ◽  
Phase Trajectory ◽  
Equilibrium Points ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Circuit Parameter ◽  
Bifurcation Diagrams ◽  
Dynamical Behaviors ◽  
Simulation Results

We propose a meminductor-based chaotic system. Theoretical analysis and numerical simulations reveal complex dynamical behaviors of the proposed meminductor-based chaotic system with five unstable equilibrium points and three different states of chaotic attractors in its phase trajectory with only a single change in circuit parameter. Lyapunov exponents, bifurcation diagrams, and phase portraits are used to investigate its complex chaotic and multi-stability behaviors, including its coexisting chaotic, periodic and point attractors. The proposed meminductor-based chaotic system was implemented using analog integrators, inverters, summers, and multipliers. PSPICE simulation results verified different chaotic characteristics of the proposed circuit with a single change in a resistor value.

Nine-Dimensional Eight-Order Chaotic System and its Circuit Implementation

2014 ◽  
Vol 716-717 ◽  
pp. 1346-1351
Author(s):  
Jian Liang Zhu ◽  
Jiang Dong ◽  
Hua Qiang Gao
Keyword(s):  
Chaotic System ◽  
Chaos Theory ◽  
High Dimensional ◽  
Chaotic Attractors ◽  
Higher Dimension ◽  
Matlab Simulation ◽  
Circuit Implementation ◽  
Dynamical Behaviors ◽  
Simulation Results ◽  
Hardware Circuit

The chaotic characteristics of high-dimensional chaotic system are more complex, so the design of chaotic system with higher dimension has become a leading subject of chaos theory. In this paper, we constructed a nine-dimensional eight-order chaotic system. Matlab simulation of system is performed and Lyapunov exponents are figured out, which proved more complex dynamical behaviors. And the corresponding hardware circuit is designed. Multisim simulation results of the circuit coincide with Matlab simulation of the system completely, showing the same chaotic attractors. The consistent results verified the realizability of system. Therefore, the system can provide a more secure encryption source for information encryption.

Complex Dynamical Behaviors in a 3D Simple Chaotic Flow with 3D Stable or 3D Unstable Manifolds of a Single Equilibrium

2019 ◽  
Vol 29 (07) ◽  
pp. 1950095 ◽  
Author(s):  
Zhouchao Wei ◽  
Yingying Li ◽  
Bo Sang ◽  
Yongjian Liu ◽  
Wei Zhang
Keyword(s):  
Periodic Solution ◽  
Chaotic Systems ◽  
Chaotic Attractors ◽  
Hidden Attractors ◽  
Chaotic Flow ◽  
Dynamical Behaviors ◽  
Unstable Manifolds ◽  
The Stability ◽  
Hyperbolic Equilibrium ◽  
Relationship Of

This paper shows some examples of chaotic systems for the six types of only one hyperbolic equilibrium in changed chameleon-like chaotic system. Two of the six cases have hidden attractors. By adjusting the parameters in the system and controlling the stability of only one equilibrium, we can further obtain chaos with four kinds of conditions: (1) index-0 node; (2) index-3 node; (3) index-0 node foci; (4) index-3 node foci. Based on the method of focus quantities, we study three limit cycles (the outmost and inner cycles are stable, and the intermediate cycle is unstable) bifurcating from an isolated Hopf equilibrium. In addition, one periodic solution can be obtained from a nonisolated zero-Hopf equilibrium. The system may help us in better understanding, revealing an intrinsic relationship of the global dynamical behaviors with the stability of equilibrium point, especially hidden chaotic attractors.

A Simple Grid Multiscroll Chaotic Electronic Oscillator Employing CFOAs

2014 ◽  
Vol 24 (02) ◽  
pp. 1450017 ◽  
Author(s):  
Yuan Lin ◽  
Chun Hua Wang ◽  
Jin Wen Yin ◽  
Yan Hu
Keyword(s):  
Theoretical Analysis ◽  
Circuit Design ◽  
Nonlinear Function ◽  
Operational Amplifiers ◽  
Chaotic Attractors ◽  
Simple Circuit ◽  
Chaotic Circuit ◽  
Current Feedback ◽  
Current Feedback Operational Amplifiers ◽  
Electronic Oscillator

In this paper, a novel grid multiscroll chaotic electronic oscillator with simple circuit design is proposed. The proposed grid multiscroll chaotic circuit only needs two current feedback operational amplifiers (CFOAs) as current integrators, passive RC, and nonlinear elements in the form of current stair nonlinear function series (SNFS) realized with CFOAs. Compared with existing grid multiscroll circuits such as Chua's circuit and Jerk circuit, etc., its component count is reduced. Mathematical models of the proposed generators are derived. Theoretical analysis and numerical simulations of the derived models are included. Moreover, the experimental results are verified that the proposed simpler chaotic electronic oscillator can generate grid multiscroll chaotic attractors with higher frequency.

scholarly journals Dynamic Behaviors Analysis of a Chaotic Circuit Based on a Novel Fractional-Order Generalized Memristor

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Ningning Yang ◽  
Shucan Cheng ◽  
Chaojun Wu ◽  
Rong Jia ◽  
Chongxin Liu
Keyword(s):  
Fractional Order ◽  
Initial Conditions ◽  
Chaotic Attractors ◽  
Chaotic Circuit ◽  
Diagram Method ◽  
Dynamic Behaviors ◽  
System Parameters ◽  
Pinched Hysteresis Loop ◽  
The Impact ◽  
The Mathematical Model

In this paper, a fractional-order chaotic circuit based on a novel fractional-order generalized memristor is proposed. It is proved that the circuit based on the diode bridge cascaded with fractional-order inductor has volt-ampere characteristics of pinched hysteresis loop. Then the mathematical model of the fractional-order memristor chaotic circuit is obtained. The impact of the order and system parameters on the dynamic behaviors of the chaotic circuit is studied by phase trajectory, Poincaré Section, and bifurcation diagram method. The order, as an important parameter, can increase the degree of freedom of the system. With the change of the order and parameters, the circuit will exhibit abundant dynamic behaviors such as coexisting upper and lower limit cycle, single scroll chaotic attractors, and double scroll chaotic attractors under different initial conditions. And the system exhibits antimonotonic behavior of antiperiodic bifurcation with the change of system parameters. The equivalent circuit simulations are designed to verify the results of the theoretical analysis and numerical simulation.

GENERATION OF MULTI-WING CHAOTIC ATTRACTORS FROM A LORENZ-LIKE SYSTEM

2013 ◽  
Vol 23 (09) ◽  
pp. 1350152 ◽  
Author(s):  
QIANG LAI ◽  
ZHI-HONG GUAN ◽  
YONGHONG WU ◽  
FENG LIU ◽  
DING-XUE ZHANG
Keyword(s):  
Theoretical Analysis ◽  
Chaotic System ◽  
Chaotic Attractors ◽  
Initial Value ◽  
Simulation Results ◽  
Switching Method

In this paper, two methods are proposed to construct multi-wing chaotic attractors based on a Lorenz-like autonomous chaotic system. The first is switching method which can directly multiply the wings of the system without segment linearization of the system. The second is coordinate transition method which is related to the initial value of the system. Moreover, theoretical analysis and simulation results show the effectiveness of these two methods.

scholarly journals A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation

Inventions ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 49
Author(s):  
Zain-Aldeen S. A. Rahman ◽  
Basil H. Jasim ◽  
Yasir I. A. Al-Yasir ◽  
Raed A. Abd-Alhameed ◽  
Bilal Naji Alhasnawi
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Real World ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
State Variables ◽  
Digital Implementation ◽  
Dynamical Behaviors ◽  
Real World Applications

In this paper, a new fractional order chaotic system without equilibrium is proposed, analytically and numerically investigated, and numerically and experimentally tested. The analytical and numerical investigations were used to describe the system’s dynamical behaviors including the system equilibria, the chaotic attractors, the bifurcation diagrams, and the Lyapunov exponents. Based on the obtained dynamical behaviors, the system can excite hidden chaotic attractors since it has no equilibrium. Then, a synchronization mechanism based on the adaptive control theory was developed between two identical new systems (master and slave). The adaptive control laws are derived based on synchronization error dynamics of the state variables for the master and slave. Consequently, the update laws of the slave parameters are obtained, where the slave parameters are assumed to be uncertain and are estimated corresponding to the master parameters by the synchronization process. Furthermore, Arduino Due boards were used to implement the proposed system in order to demonstrate its practicality in real-world applications. The simulation experimental results were obtained by MATLAB and the Arduino Due boards, respectively, with a good consistency between the simulation results and the experimental results, indicating that the new fractional order chaotic system is capable of being employed in real-world applications.

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