scholarly journals A Novel Memristor Chaotic System with a Hidden Attractor and Multistability and Its Implementation in a Circuit

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Lili Huang ◽  
Yanling Wang ◽  
Yicheng Jiang ◽  
Tengfei Lei
Keyword(s):  
Chaotic System ◽  
Initial Conditions ◽  
Hidden Attractor ◽  
Extreme Multistability ◽  
Transient Period ◽  
Tangent Function ◽  
Infinite Line ◽  
Hardware Circuit ◽  
Self Replication ◽  
Active Flux

By introducing an ideal and active flux-controlled memristor and tangent function into an existing chaotic system, an interesting memristor-based self-replication chaotic system is proposed. The most striking feature is that this system has infinite line equilibria and exhibits the extreme multistability phenomenon of coexisting infinitely many attractors. In this paper, bifurcation diagrams and Lyapunov exponential spectrum are used to analyze in detail the influence of various parameter changes on the dynamic behavior of the system; it shows that the newly proposed chaotic system has the phenomenon of alternating chaos and limit cycle. Especially, transition behavior of the transient period with steady chaos can be also found for some initial conditions. Moreover, a hardware circuit is designed by PSpice and fabricated, and its experimental results effectively verify the truth of extreme multistability.

scholarly journals Composite One- to Six-Scroll Hidden Attractors in a Memristor-Based Chaotic System and Their Circuit Implementation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Ying Li ◽  
Xiaozhu Xia ◽  
Yicheng Zeng ◽  
Qinghui Hong
Keyword(s):  
Fixed Point ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Circuit Implementation ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Extreme Multistability ◽  
Different Types ◽  
Hardware Circuit ◽  
New System

Chaotic systems with hidden multiscroll attractors have received much attention in recent years. However, most parts of hidden multiscroll attractors previously reported were repeated by the same type of attractor, and the composite of different types of attractors appeared rarely. In this paper, a memristor-based chaotic system, which can generate composite attractors with one up to six scrolls, is proposed. These composite attractors have different forms, similar to the Chua’s double scroll and jerk double scroll. Through theoretical analysis, we find that the new system has no fixed point; that is to say, all of the composite multiscroll attractors are hidden attractors. Additionally, some complicated dynamic behaviors including various hidden coexisting attractors, extreme multistability, and transient transition are explored. Moreover, hardware circuit using discrete components is implemented, and its experimental results supported the numerical simulations results.

scholarly journals Study on Bias Control of Memristor Multistablity System

2021 ◽  
Vol 233 ◽  
pp. 04002
Author(s):  
Hongyan Zang ◽  
Lili Huang ◽  
Yanling Wang ◽  
Tengfei Lei
Keyword(s):  
Periodic Function ◽  
Power Control ◽  
Chaotic System ◽  
Analog Circuit ◽  
Initial Conditions ◽  
Hidden Attractor ◽  
Output Variable ◽  
Dc Power ◽  
Signal Polarity ◽  
Sinusoidal Function

In this paper, we study a memristor chaotic system with bias control. Based on the analysis of basic dynamic behavior, the hidden attractor coexistence and multi-stability of the non-equilibrium memristor chaotic system are verified, the bias control based on DC power control is studied, and the polarity control of the output variable is realized by using the change of parameters. The sinusoidal function is introduced as the bias periodic function, so that the system can realize signal polarity control only by changing the initial conditions. The analog circuit of memristor chaotic system is designed and verified by simulation..

Hidden Extreme Multistability, Antimonotonicity and Offset Boosting Control in a Novel Fractional-Order Hyperchaotic System Without Equilibrium

2018 ◽  
Vol 28 (13) ◽  
pp. 1850167 ◽  
Author(s):  
Sen Zhang ◽  
Yicheng Zeng ◽  
Zhijun Li ◽  
Chengyi Zhou
Keyword(s):  
Fractional Order ◽  
Initial Conditions ◽  
State Feedback Control ◽  
Hyperchaotic System ◽  
Hidden Attractors ◽  
System Parameters ◽  
Offset Boosting ◽  
Extreme Multistability ◽  
Hidden Extreme Multistability ◽  
New System

Recently, the notion of hidden extreme multistability and hidden attractors is very attractive in chaos theory and nonlinear dynamics. In this paper, by utilizing a simple state feedback control technique, a novel 4D fractional-order hyperchaotic system is introduced. Of particular interest is that this new system has no equilibrium, which indicates that its attractors are all hidden and thus Shil’nikov method cannot be applied to prove the existence of chaos for lacking hetero-clinic or homo-clinic orbits. Compared with other fractional-order chaotic or hyperchaotic systems, this new system possesses three unique and remarkable features: (i) The amazing and interesting phenomenon of the coexistence of infinitely many hidden attractors with respect to same system parameters and different initial conditions is observed, meaning that hidden extreme multistability arises. (ii) By varying the initial conditions and selecting appropriate system parameters, the striking phenomenon of antimonotonicity is first discovered, especially in such a fractional-order hyperchaotic system without equilibrium. (iii) An attractive special feature of the convenience of offset boosting control of the system is also revealed. The complex and rich hidden dynamic behaviors of this system are investigated by using conventional nonlinear analysis tools, including equilibrium stability, phase portraits, bifurcation diagram, Lyapunov exponents, spectral entropy complexity, and so on. Furthermore, a hardware electronic circuit is designed and implemented. The hardware experimental results and the numerical simulations of the same system on the Matlab platform are well consistent with each other, which demonstrates the feasibility of this new fractional-order hyperchaotic system.

scholarly journals An Efficient Method of Image Encryption Using Rossler Chaotic System

2021 ◽  
Vol 10 (2) ◽  
pp. 11
Author(s):  
Yasir Ahmed Hamza ◽  
Marwan Dahar Omer
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Initial Conditions ◽  
Computation Time ◽  
Encryption Algorithm ◽  
Brute Force ◽  
Symmetric Encryption ◽  
New Approach ◽  
System Parameters ◽  
Plain Image

In this study, a new approach of image encryption has been proposed. This method is depends on the symmetric encryption algorithm RC4 and Rossler chaotic system. Firstly, the encryption key is employed to ciphering a plain image using RC4 and obtains a ciphered-image. Then, the same key is used to generate the initial conditions of the Rossler system. The system parameters and the initial conditions are used as the inputs for Rossler chaotic system to generate the 2-dimensional array of random values. The resulted array is XORed with the ciphered-image to obtain the final encrypted-image. Based on the experimental results, the proposed method has achieved high security and less computation time. Also, the proposed method can be resisted attacks like (statistical, brute-force, and differential).

scholarly journals Dynamic Analysis and Cryptographic Application of a Sinusoidal-polynomial Composite Chaotic System

2021 ◽  
Author(s):  
Hegui Zhu ◽  
Jiangxia Ge ◽  
Wentao Qi ◽  
Xiangde Zhang ◽  
Xiaoxiong Lu
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Encryption Algorithm ◽  
Topological Transitivity ◽  
Detailed Simulation ◽  
Definition Of ◽  
Image Encryption Algorithm ◽  
Sensitivity To Initial Conditions

Abstract Owning to complex properties of ergodicity, non-periodic ability and sensitivity to initial states, chaotic systems are widely used in cryptography. In this paper, we propose a sinusoidal--polynomial composite chaotic system (SPCCS), and prove that it satisfies Devaney's definition of chaos: the sensitivity to initial conditions, topological transitivity and density of periodic points. The experimental results show that the SPCCS has better unpredictability and more complex chaotic behavior than the classical chaotic maps. Furthermore, we provide a new image encryption algorithm combining pixel segmentation operation, block chaotic matrix confusing operation, and pixel diffusion operation with the SPCCS. Detailed simulation results verify effectiveness of the proposed image encryption algorithm.

Difference Synchronization of Identical and Nonidentical Chaotic and Hyperchaotic Systems of Different Orders Using Active Backstepping Design

2018 ◽  
Vol 13 (5) ◽  
Author(s):  
Eric Donald Dongmo ◽  
Kayode Stephen Ojo ◽  
Paul Woafo ◽  
Abdulahi Ndzi Njah
Keyword(s):  
Chaotic System ◽  
Initial Conditions ◽  
Lyapunov Stability Theory ◽  
The State ◽  
State Variables ◽  
State Variable ◽  
New Type ◽  
The Difference ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems

This paper introduces a new type of synchronization scheme, referred to as difference synchronization scheme, wherein the difference between the state variables of two master [slave] systems synchronizes with the state variable of a single slave [master] system. Using the Lyapunov stability theory and the active backstepping technique, controllers are derived to achieve the difference synchronization of three identical hyperchaotic Liu systems evolving from different initial conditions, as well as the difference synchronization of three nonidentical systems of different orders, comprising the 3D Lorenz chaotic system, 3D Chen chaotic system, and the 4D hyperchaotic Liu system. Numerical simulations are presented to demonstrate the validity and feasibility of the theoretical analysis. The development of difference synchronization scheme has increases the number of existing chaos synchronization scheme.

Image Encryption Algorithm Based on a Novel 4D Chaotic System

2021 ◽  
Vol 15 (4) ◽  
pp. 118-131
Author(s):  
Sadiq A. Mehdi
Keyword(s):  
Chaotic System ◽  
Initial Conditions ◽  
High Sensitivity ◽  
Encryption Algorithm ◽  
Pseudorandom Sequence ◽  
Key Space ◽  
Xor Operation ◽  
Change Intensity ◽  
And Performance ◽  
Image Cryptosystem

In this paper, a novel four-dimensional chaotic system has been created, which has characteristics such as high sensitivity to the initial conditions and parameters. It also has two a positive Lyapunov exponents. This means the system is hyper chaotic. In addition, a new algorithm was suggested based on which they constructed an image cryptosystem. In the permutation stage, the pixel positions are scrambled via a chaotic sequence sorting. In the substitution stage, pixel values are mixed with a pseudorandom sequence generated from the 4D chaotic system using XOR operation. A simulation has been conducted to evaluate the algorithm, using the standardized tests such as information entropy, histogram, number of pixel change rate, unified average change intensity, and key space. Experimental results and performance analyses demonstrate that the proposed encryption algorithm achieves high security and efficiency.

A Compact and Low Power Realization of a High Frequency Chaotic Oscillator

2017 ◽  
Vol 2017 (DPC) ◽  
pp. 1-27
Author(s):  
R. Chase Harrison ◽  
Benjamin K. Rhea ◽  
Frank T. Werner ◽  
Robert N. Dean
Keyword(s):  
Low Power ◽  
Chaotic System ◽  
High Frequency ◽  
High Speed ◽  
Random Number ◽  
Nonlinear Dynamical Systems ◽  
Initial Conditions ◽  
Random Number Generation ◽  
Chaotic Oscillator ◽  
Number Generation

The desirable properties exhibited in some nonlinear dynamical systems have many potential uses. These properties include sensitivity to initial conditions, wide bandwidth, and long-term aperiodicity, which lend themselves to applications such as random number generation, communication and audio ranging systems. Chaotic systems can be realized in electronics by using inexpensive and readily available parts. Many of these systems have been verified in electronics using nonpermanent prototyping at very low frequencies; however, this restricts the range of potential applications. In particular, random number generation (RNG) benefits from an increase in operation frequency, since it is proportional to the amount of bits that can be produced per second. This work looks specifically at the nonlinear element in the chaotic system and evaluates its frequency limitations in electronics. In practice, many of nonlinearities are difficult to implement in high speed electronics. In addition to this restriction, the use of complex feedback paths and large inductors prevents the miniaturization that is desirable for implementing chaotic circuits in other electronic systems. By carefully analyzing the fundamental dynamics that govern the chaotic system, these problems can be addressed. Presented in this work is the design and realization of a high frequency chaotic oscillator that exhibits complex and rich dynamics while using a compact footprint and low power consumption.

scholarly journals A Survey on True Random Number Generators Based on Chaos

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Fei Yu ◽  
Lixiang Li ◽  
Qiang Tang ◽  
Shuo Cai ◽  
Yun Song ◽  
...  
Keyword(s):  
Chaotic System ◽  
Key Management ◽  
Random Number ◽  
Initial Conditions ◽  
Rapid Development ◽  
Current Mode ◽  
Random Numbers ◽  
Random Number Generators ◽  
Network Information ◽  
Survey Paper

With the rapid development of communication technology and the popularization of network, information security has been highly valued by all walks of life. Random numbers are used in many cryptographic protocols, key management, identity authentication, image encryption, and so on. True random numbers (TRNs) have better randomness and unpredictability in encryption and key than pseudorandom numbers (PRNs). Chaos has good features of sensitive dependence on initial conditions, randomness, periodicity, and reproduction. These demands coincide with the rise of TRNs generating approaches in chaos field. This survey paper intends to provide a systematic review of true random number generators (TRNGs) based on chaos. Firstly, the two kinds of popular chaotic systems for generating TRNs based on chaos, including continuous time chaotic system and discrete time chaotic system are introduced. The main approaches and challenges are exposed to help researchers decide which are the ones that best suit their needs and goals. Then, existing methods are reviewed, highlighting their contributions and their significance in the field. We also devote a part of the paper to review TRNGs based on current-mode chaos for this problem. Finally, quantitative results are given for the described methods in which they were evaluated, following up with a discussion of the results. At last, we point out a set of promising future works and draw our own conclusions about the state of the art of TRNGs based on chaos.

Sign in / Sign up

Export Citation Format

Share Document