Generating Four-Wing Hyperchaotic Attractor and Two-Wing, Three-Wing, and Four-Wing Chaotic Attractors in 4D Memristive System

2017 ◽  
Vol 27 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Ling Zhou ◽  
Chunhua Wang ◽  
Lili Zhou
Keyword(s):  
Chaotic System ◽  
Three Dimensional ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Hyperchaotic System ◽  
Multiple Attractors ◽  
System A ◽  
Dynamical Behaviors ◽  
Memristive System ◽  
Line Of Equilibria

By adding only one smooth flux-controlled memristor into a three-dimensional (3D) pseudo four-wing chaotic system, a new real four-wing hyperchaotic system is constructed in this paper. It is interesting to see that this new memristive chaotic system can generate a four-wing hyperchaotic attractor with a line of equilibria. Moreover, it can generate two-, three- and four-wing chaotic attractors with the variation of a single parameter which denotes the strength of the memristor. At the same time, various coexisting multiple attractors (e.g. three-wing attractors, four-wing attractors and attractors with state transition under the same system parameters) are observed in this system, which means that extreme multistability arises. The complex dynamical behaviors of the proposed system are analyzed by Lyapunov exponents (LEs), phase portraits, Poincaré maps, and time series. An electronic circuit is finally designed to implement the hyperchaotic memristive system.

A NEW CHAOTIC SYSTEM AND BEYOND: THE GENERALIZED LORENZ-LIKE SYSTEM

2004 ◽  
Vol 14 (05) ◽  
pp. 1507-1537 ◽  
Author(s):  
JINHU LÜ ◽  
GUANRONG CHEN ◽  
DAIZHAN CHENG
Keyword(s):  
Chaotic System ◽  
Chaotic Attractor ◽  
Three Dimensional ◽  
Chaotic Attractors ◽  
Compound Structure ◽  
Constant Input ◽  
New Class ◽  
Dynamical Behaviors ◽  
Generalized Lorenz System ◽  
New Chaotic System

This article introduces a new chaotic system of three-dimensional quadratic autonomous ordinary differential equations, which can display (i) two 1-scroll chaotic attractors simultaneously, with only three equilibria, and (ii) two 2-scroll chaotic attractors simultaneously, with five equilibria. Several issues such as some basic dynamical behaviors, routes to chaos, bifurcations, periodic windows, and the compound structure of the new chaotic system are then investigated, either analytically or numerically. Of particular interest is the fact that this chaotic system can generate a complex 4-scroll chaotic attractor or confine two attractors to a 2-scroll chaotic attractor under the control of a simple constant input. Furthermore, the concept of generalized Lorenz system is extended to a new class of generalized Lorenz-like systems in a canonical form. Finally, the important problems of classification and normal form of three-dimensional quadratic autonomous chaotic systems are formulated and discussed.

scholarly journals Chaos-Based Application of a Novel Multistable 5D Memristive Hyperchaotic System with Coexisting Multiple Attractors

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-19 ◽  
Author(s):  
Fei Yu ◽  
Li Liu ◽  
Shuai Qian ◽  
Lixiang Li ◽  
Yuanyuan Huang ◽  
...  
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Random Number Generator ◽  
Phase Portraits ◽  
Hyperchaotic System ◽  
The Novel ◽  
Multiple Attractors ◽  
Period 2 ◽  
Different Types ◽  
System Designs

Novel memristive hyperchaotic system designs and their engineering applications have received considerable critical attention. In this paper, a novel multistable 5D memristive hyperchaotic system and its application are introduced. The interesting aspect of this chaotic system is that it has different types of coexisting attractors, chaos, hyperchaos, periods, and limit cycles. First, a novel 5D memristive hyperchaotic system is proposed by introducing a flux-controlled memristor with quadratic nonlinearity into an existing 4D four-wing chaotic system as a feedback term. Then, the phase portraits, Lyapunov exponential spectrum, bifurcation diagram, and spectral entropy are used to analyze the basic dynamics of the 5D memristive hyperchaotic system. For a specific set of parameters, we find an unusual metastability, which shows the transition from chaotic to periodic (period-2 and period-3) dynamics. Moreover, its circuit implementation is also proposed. By using the chaoticity of the novel hyperchaotic system, we have developed a random number generator (RNG) for practical image encryption applications. Furthermore, security analyses are carried out with the RNG and image encryption designs.

DYNAMICAL ANALYSIS OF A CHAOTIC SYSTEM WITH TWO DOUBLE-SCROLL CHAOTIC ATTRACTORS

2004 ◽  
Vol 14 (03) ◽  
pp. 971-998 ◽  
Author(s):  
WENBO LIU ◽  
GUANRONG CHEN
Keyword(s):  
Chaotic System ◽  
Three Dimensional ◽  
Dynamical Analysis ◽  
Chaotic Attractors ◽  
Compound Structure ◽  
Numerical Examples ◽  
Routes To Chaos ◽  
Basic Properties ◽  
Dynamical Behaviors

Dynamical behaviors of a three-dimensional autonomous chaotic system with two double-scroll attractors are studied. Some basic properties such as bifurcation, routes to chaos, periodic windows and compound structure are demonstrated with various numerical examples. System equilibria and their stabilities are discussed, and chaotic features of the attractors are justified numerically.

scholarly journals Circuit Implementation, Synchronization of Multistability, and Image Encryption of a Four-Wing Memristive Chaotic System

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Guangya Peng ◽  
Fuhong Min ◽  
Enrong Wang
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Secure Communication ◽  
Secret Key ◽  
Multiple Attractors ◽  
Dynamical Behaviors ◽  
Key Space ◽  
Control Scheme ◽  
Memristive System ◽  
Coexistence Of Multiple Attractors

The four-wing memristive chaotic system used in synchronization is applied to secure communication which can increase the difficulty of deciphering effectively and enhance the security of information. In this paper, a novel four-wing memristive chaotic system with an active cubic flux-controlled memristor is proposed based on a Lorenz-like circuit. Dynamical behaviors of the memristive system are illustrated in terms of Lyapunov exponents, bifurcation diagrams, coexistence Poincaré maps, coexistence phase diagrams, and attraction basins. Besides, the modular equivalent circuit of four-wing memristive system is designed and the corresponding results are observed to verify its accuracy and rationality. A nonlinear synchronization controller with exponential function is devised to realize synchronization of the coexistence of multiple attractors, and the synchronization control scheme is applied to image encryption to improve secret key space. More interestingly, considering different influence of multistability on encryption, the appropriate key is achieved to enhance the antideciphering ability.

CONSTRUCTING MULTIWING HYPERCHAOTIC ATTRACTORS

2010 ◽  
Vol 20 (03) ◽  
pp. 727-734 ◽  
Author(s):  
BO YU ◽  
GUOSI HU
Keyword(s):  
Numerical Simulation ◽  
Chaotic System ◽  
Topological Structure ◽  
Construction Method ◽  
Chaotic Attractors ◽  
Hyperchaotic System ◽  
Simple Construction ◽  
System A ◽  
New Hyperchaotic System ◽  
New System

Few reports have introduced chaotic attractors with both multiwing topological structure and hyperchaotic dynamics. A simple construction method, for designing chaotic system with multiwing attractors, is presented in this paper. The number of wings in the attractor was doubled on applying this method to an arbitrary smooth chaotic system. Moreover, the hyperchaotic property is preserved in the new system. A new hyperchaotic system with 16-wing attractors is constructed; the result system is not only verified via numerical simulation but also confirmed by a DSP-based experiment.

scholarly journals Three-Dimensional Memristive Hindmarsh–Rose Neuron Model with Hidden Coexisting Asymmetric Behaviors

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Bocheng Bao ◽  
Aihuang Hu ◽  
Han Bao ◽  
Quan Xu ◽  
Mo Chen ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Electromagnetic Induction ◽  
Neuron Model ◽  
Complex Dynamics ◽  
Three Dimensional ◽  
Phase Portraits ◽  
Neuronal System ◽  
System A ◽  
Dynamical Behaviors ◽  
Electrical Activities

Since the electrical activities of neurons are closely related to complex electrophysiological environment in neuronal system, a novel three-dimensional memristive Hindmarsh–Rose (HR) neuron model is presented in this paper to describe complex dynamics of neuronal activities with electromagnetic induction. The proposed memristive HR neuron model has no equilibrium point but can show hidden dynamical behaviors of coexisting asymmetric attractors, which has not been reported in the previous references for the HR neuron model. Mathematical model based numerical simulations for hidden coexisting asymmetric attractors are performed by bifurcation analyses, phase portraits, attraction basins, and dynamical maps, which just demonstrate the occurrence of complex dynamical behaviors of electrical activities in neuron with electromagnetic induction. Additionally, circuit breadboard based experimental results well confirm the numerical simulations.

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.

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 New Fractional Order Chaotic System: Analysis, Synchronization, and it’s Application

2021 ◽  
Vol 17 (1) ◽  
pp. 1-9
Author(s):  
Zain_Aldeen Rahman ◽  
Basil Jassim ◽  
Yasir Al_Yasir
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Secure Communication ◽  
System Analysis ◽  
Three Dimensional ◽  
Nonlinear Dynamic System ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Communication Scheme ◽  
New System

In this paper, a new nonlinear dynamic system, new three-dimensional fractional order complex chaotic system, is presented. This new system can display hidden chaotic attractors or self-excited chaotic attractors. The Dynamic behaviors of this system have been considered analytically and numerically. Different means including the equilibria, chaotic attractor phase portraits, the Lyapunov exponent, and the bifurcation diagrams are investigated to show the chaos behavior in this new system. Also, a synchronization technique between two identical new systems has been developed in master- slave configuration. The two identical systems are synchronized quickly. Furthermore, the master-slave synchronization is applied in secure communication scheme based on chaotic masking technique. In the application, it is noted that the message is encrypted and transmitted with high security in the transmitter side, in the other hand the original message has been discovered with high accuracy in the receiver side. The corresponding numerical simulation results proved the efficacy and practicability of the developed synchronization technique and its application

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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