ArticlePublisher preview available

A new four-dimensional memristive system, synchronization and its application in image encryption

Authors:
Xiaojun Liu at Nanjing Tech University
Xiaojun Liu
Pu Wang
Pu Wang
Pu Wang
  • This person is not on ResearchGate, or hasn't claimed this research yet.
Dafeng Tang at Xi’an University of Posts and Telecommunications
Dafeng Tang
Jing Tian
Jing Tian
Jing Tian
  • This person is not on ResearchGate, or hasn't claimed this research yet.
Read publisher preview
Download citation
To read the full-text of this research, you can request a copy directly from the authors.

Abstract and Figures

In this paper, a new four-dimensional (4D) memristive system is presented by introducing a memristor equation to a 3D chaotic system. Firstly, the basic characteristics including existence and stability of equilibrium points, and Kaplan–Yoke dimension for the memristive system are analyzed from a theoretical perspective. The description of the 4D memristive system in the integer-order and the fractional-order cases is given. In both cases, the dynamics with the variation of a system parameter or a derivative order is studied by the numerical simulations. The results show that the integer-order and the fractional-order memristive systems have rich dynamics. Secondly, in order to realize the synchronization for the memristive system, two adaptive synchronization schemes are designed, namely, the identical structure and the different structure synchronization. Numerical simulation results show that the designed synchronization controllers are effective. Finally, a novel image encryption algorithm is expanded to the image encryption for color images based on the memristive system. The simulation results demonstrate the image encryption method based on the memristive system has a perfect encryption effect for the color images.
Chaotic attractors of system (2). a a chaotic attractor in a 3D space; b the projection of the chaotic attractor in x–y plane
Chaotic attractors of system (2). a a chaotic attractor in a 3D space; b the projection of the chaotic attractor in x–y plane
… 
Dynamics of the system with different values of parameter a. a Bifurcation diagram versus parameter a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a$$\end{document}; b Lyapunov exponents spectrum with the variation of parameter a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a$$\end{document}; c phase diagram for a=0.11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a = 0.11$$\end{document}; d phase diagram for a=0.2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a = 0.2$$\end{document}; e phase diagram for a=0.3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a = 0.3$$\end{document}
Dynamics of the system with different values of parameter a. a Bifurcation diagram versus parameter a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a$$\end{document}; b Lyapunov exponents spectrum with the variation of parameter a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a$$\end{document}; c phase diagram for a=0.11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a = 0.11$$\end{document}; d phase diagram for a=0.2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a = 0.2$$\end{document}; e phase diagram for a=0.3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a = 0.3$$\end{document}
… 
Dynamics of the system with different values of parameter b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b$$\end{document}. a Bifurcation diagram versus parameter b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b$$\end{document}; b Lyapunov exponents spectrum with the variation of parameter b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b$$\end{document}; c phase diagram for b=0.175\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b = 0.175$$\end{document}; d phase diagram for b=0.2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b = 0.2$$\end{document}; e phase diagram for b=0.25\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b = 0.25$$\end{document}
Dynamics of the system with different values of parameter b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b$$\end{document}. a Bifurcation diagram versus parameter b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b$$\end{document}; b Lyapunov exponents spectrum with the variation of parameter b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b$$\end{document}; c phase diagram for b=0.175\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b = 0.175$$\end{document}; d phase diagram for b=0.2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b = 0.2$$\end{document}; e phase diagram for b=0.25\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b = 0.25$$\end{document}
… 
Bifurcation diagrams of system (2) in the three-dimensional space. a the bifurcation diagrams versus b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b$$\end{document} when the parameter a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a$$\end{document} is varied; b the bifurcation diagrams versus a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a$$\end{document} when the parameter b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b$$\end{document} is varied
Bifurcation diagrams of system (2) in the three-dimensional space. a the bifurcation diagrams versus b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b$$\end{document} when the parameter a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a$$\end{document} is varied; b the bifurcation diagrams versus a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a$$\end{document} when the parameter b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b$$\end{document} is varied
… 
Chaotic attractor projected on the x–y plane of system (15)
+8
Chaotic attractor projected on the x–y plane of system (15)
… 
Figures - available from: International Journal of Dynamics and Control
This content is subject to copyright. Terms and conditions apply.
A preview of this full-text is provided by Springer Nature.
Learn more
Content available from International Journal of Dynamics and Control
This content is subject to copyright. Terms and conditions apply.
International Journal of Dynamics and Control (2024) 12:3669–3684
https://doi.org/10.1007/s40435-024-01464-x
A new four-dimensional memristive system, synchronization and its
application in image encryption
Xiaojun Liu1·Pu Wang1·Dafeng Tang2·Jing Tian1
Received: 24 April 2024 / Revised: 12 June 2024 / Accepted: 14 June 2024 / Published online: 26 June 2024
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024
Abstract
In this paper, a new four-dimensional (4D) memristive system is presented by introducing a memristor equation to a 3D
chaotic system. Firstly, the basic characteristics including existence and stability of equilibrium points, and Kaplan–Yoke
dimension for the memristive system are analyzed from a theoretical perspective. The description of the 4D memristive
system in the integer-order and the fractional-order cases is given. In both cases, the dynamics with the variation of a
system parameter or a derivative order is studied by the numerical simulations. The results show that the integer-order
and the fractional-order memristive systems have rich dynamics. Secondly, in order to realize the synchronization for the
memristive system, two adaptive synchronization schemes are designed, namely, the identical structure and the different
structure synchronization. Numerical simulation results show that the designed synchronization controllers are effective.
Finally, a novel image encryption algorithm is expanded to the image encryption for color images based on the memristive
system. The simulation results demonstrate the image encryption method based on the memristive system has a perfect
encryption effect for the color images.
Keywords Chaos ·Bifurcation ·A 4D memristive system ·Synchronization ·Image encryption
1 Introduction
Chaos, which exists in wide engineering fields, is considered
as a complex nonlinear dynamics phenomenon. It is a hot
topic of nonlinear dynamics in the past hundred years. On the
one side, we want to avoid chaos in some fields of engineer-
ing for its characteristic. On the other side, chaotic property
can be applied in secure communication in order to enhance
the security of information [1–5]. These extensive and deep
researches lead to a large number of areas of implementa-
tion related to nonlinear systems with chaotic characteristic.
Many chaotic systems are introduced and studied deeply,
such as Lorenz system, Rössler system, Chen system, Chua
circuit, and so on [6–11]. As we known that the memris-
tive device can store and adjust resistance values. Therefore,
memristors have been widely used to design a broad category
BXiaojun Liu
flybett3952@126.com
1School of Sciences, Xi’an University of Posts and
Telecommunications, Xi’an 710061, China
2School of Automation, Xi’an University of Posts and
Telecommunications, Xi’an 710061, China
of nonlinear systems, including nonvolatile memory, mem-
ristive neural networks, chaotic circuits and so on [12–16].
As a kind of important and complicated chaotic circuit sys-
tems, the dynamics of memristive systems has been studied
deeply [17–20].
Generally speaking, 4D or higher dimensional systems
have more complicated dynamics, especially the hyper-
chaotic property. This kind of systems can be obtained when
a memristor equation or a nonlinear feedback controller is
introduced into a dynamical system [21–24]. Both technics
enable us to move from a 3D system to a 4D system. A
number of 4D or 5D chaotic systems were proposed and
investigated in [25–27]. In [25], a new 4D no-equilibrium
chaotic system with infinitely many coexisting hidden attrac-
tors was proposed by injecting a sinusoidal function into an
existing 4D system. Abundant dynamics including chaotic,
quasiperiodic, periodic motions, and a large number of hid-
den attractors exist in the presented systems. In [26], a
novel no-equilibrium 5D memristive hyperchaotic system
was achieved by introducing an ideal flux-controlled mem-
ristor model into an improved 4D self-excited hyperchaotic
system. An autonomous 4D memristive chaotic Sprott B
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
... In literature, many chaotic systems are studied for this application. Chaotic system [5,6] and hyper-chaotic system [7] are used to secure confidential information. One more application of chaotic systems is to generate random numbers. ...
A generalized approach to maximize the complexity of a chaotic system and its application
Article
Full-text available
  • Jan 2025
The degree of complexity and chaoticness of a chaotic system are, respectively, measured by the Lyapunov dimension and the largest Lyapunov exponent of the system. An increase in these two quantities makes a chaotic system a worthy candidate for different chaos-based applications. This paper provides a generalized methodology to find a set of parameters and initial conditions of any chaotic system that results in the maximum Lyapunov dimension. The proposed approach is validated by maximizing the Lyapunov dimension of the well-known Lorenz system. Competitive swarm optimization is chosen to realize the above objective. The maximum Lyapunov dimension of 2.169 is found for the Lorenz system. Furthermore, in the process of maximization of the Lyapunov dimension, the highest Lyapunov exponent of the Lorenz system is obtained as 7.9138. Thus, the prediction time of the Lorenz system, with the considered parameters and initial conditions, reduces. To the best of our knowledge, our results are the highest among the existing Lyapunov dimension and positive Lyapunov exponent of the Lorenz system. The significance of the increased Lyapunov dimension is demonstrated by using it in an image encryption process. To validate the proposed generalized approach, two more chaotic systems are considered to get higher Lyapunov dimensions. Extensive simulations and analyses are done and presented to substantiate the claims.
View
S-box using fractional-order 4D hyperchaotic system and its application to RSA cryptosystem-based color image encryption
Article
  • Feb 2025
  • COMPUT STAND INTER
An algorithm for substitution box (S-box) construction is proposed by using fractional-order (FO) 4D hyperchaotic system in this paper. Based on hyperchaotic sequences generated by the FO 4D hyperchaotic system, exclusive-or operations, and permutation the S-box is constructed. A comprehensive evaluation based on various algebraic criteria demonstrates that the proposed S-box exhibits favorable performance in terms of strict avalanche criterion, differential approximation probability, nonlinearity, bit independence criterion, linear approximation probability, fixed point, reverse fixed point, and correlation immunity. The proposed S-box exhibits excellent nonlinearity of 112, comparable to that of the Advanced Encryption Standard S-box. Furthermore, a novel color image encryption technique is developed to ensure the privacy of color images. The proposed color image encryption algorithm combines Arnold Cat map, a high-performance generated S-box, Rivest-Shamir-Adleman algorithm with 2D Henon chaotic map. Through rigorous testing, analysis, and comparison with recently reported image encryption algorithms, the suggested algorithm demonstrates its security, efficiency, and resistance to different standard attacks. Notably, the suggested algorithm for color image encryption offers a substantial key space and achieves an approximate correlation of 0 between adjacent pixels. Additionally, the entropy approaches the ideal value of 8.
View
Dynamics analysis and hardware implementation of multi-scroll hyperchaotic hidden attractors based on locally active memristive Hopfield neural network
Article
Full-text available
  • Dec 2023
  • NONLINEAR DYNAM
It is believed that local activation is the origin of all complexities, and the locally active memristive synaptic neural network can generate complex chaotic dynamic behaviors, such as hyperchaotic, multi-scroll, multi-stability and hidden dynamical behaviors. However, there are few studies on the simultaneous occurrence of multiple complex dynamic behaviors in neural networks. No chaotic system of multi-scroll hyperchaotic hidden attractors based on neural network has been found yet. To solve the problem, in this paper, we propose a new locally active memristive Hopfield neural network (HNN) model based on a multi-segment function, which is affected by electromagnetic radiation and external current. The multi-scroll hyperchaotic hidden attractors are found in the memristive HNN for the first time. Theoretical analysis and numerical simulation results show that the memristive HNN model has no equilibrium point, and the number of multi-scroll attractors is controlled by the state equation parameters of the memristive synapse. In addition, the structures and number of scrolls are also affected by electromagnetic radiation and external current. At the same time, under the appropriate parameter conditions, by modifying the initial value of the system, the memristive HNN has a controllable number of coexisting attractors, showing extreme multi-stability. Finally, a memristive HNN analog circuit is designed. The hardware experiment results reproduce the multi-scroll dynamics phenomenon, which verifies the correctness of the theoretical analysis and numerical simulation.
View
A hybrid color image encryption method based on extended logistic map
Article
Full-text available
The existence of images containing our personal data or strategic information of states in the developing digital world is an indication that there will be malicious people who want to access this information. Undoubtedly, the attackers’ job will be a little more difficult if the valuable information of importance is transmitted by encrypting on common channels. In this regard, traditional and modern methods are used for encryption. Although traditional cryptosystems are widely used in text encryption processes, they are rarely used in image encryption processes for two reasons. The first is that the encryption process takes a long time due to the fact that the image size is larger than the text size. The second is that, while there are fewer data losses on the text in the decryption process, data losses on the image may cause the image’s structure to be disrupted. In this study, after giving brief information about encryption, the proposed hybrid image encryption method has been explained. In this method, firstly, an encryption process performed with affine and substitution methods from traditional cryptosystems has been applied, then an extended one-dimension (1D) chaotic map has been used to strengthen the encryption process. The superiority of the proposed method has been evaluated with performance analysis.
View
A New 4D Chaos System with an Encryption Algorithm for Color and Grayscale Images
Article
Full-text available
In this paper, a new 4D chaos system is introduced based on the mathematical structure through composing and transferring. The behavior of the proposed chaotic system is studied using different tests, such as Lyapunov exponent, bifurcation diagram and histogram. In order to show the advantage of the new chaos system, the proposed system is used for image encryption. In the proposed algorithm, in addition to the new chaos system, cellular automata is also used to improve the security of the algorithm. The proposed algorithm has a separate structure for encryption key, which increases the security of the proposed algorithm. The security of the proposed environment which is evaluated using different types of security tests shows the efficiency of the proposed algorithm.
View
Quasi-synchronization of stochastic memristive neural networks subject to deception attacks
Article
Full-text available
  • Oct 2022
  • NONLINEAR DYNAM
In this paper, the quasi-synchronization problem of stochastic memristive neural networks (MNNs) subject to deception attacks is investigated via hybrid impulsive control. Deception attacks in the MNN synchronization model, which involve the attacker attempting to inject some false data into sensor-to-controller channels to destroy the control signal, are investigated from the perspective of network communication security. The attack conditions are described using stochastic variables that obey the Bernoulli distribution. Inspired by existing impulsive differential inequalities, a new inequality is proposed, which is useful for dealing with quasi-synchronization in impulsive systems. Thereafter, sufficient conditions and the error bound are obtained for validating the quasi-synchronization of stochastic MNNs subject to deception attacks based on the proposed inequality and Lyapunov stability theory. In the absence of an attack, the globally complete synchronization problem for stochastic MNNs is investigated. Additionally, the attack effects and their mitigation through control parameter design are discussed. Finally, the simulation results are presented to validate the theoretical analysis.
View
Multistable dynamics and control of a new 4D memristive chaotic Sprott B system
Article
Full-text available
  • Feb 2022
  • CHAOS SOLITON FRACT
This work proposes and investigates the dynamic behavior of a new memristive chaotic Sprott B system. One of the interesting features of this system is that it has a bias term that can adjust the symmetry of the proposed model, inducing both homogeneous and heterogeneous behaviors. Indeed, the introduced memristive system can turn from rotational symmetry (RS) to rotational symmetry broken (RSB) system in the presence or the absence of this bias term. In the RS system (i.e., absence of the bias term), pairs of symmetric attractors are formed, and the scenario of attractor merging is observed. Coexisting symmetric attractors and bifurcations with up to four solutions are perfectly investigated. In the RSB system (i.e., the bias term is non-zero), many interesting phenomena are demonstrated, including asymmetric attractors, coexisting asymmetric bifurcations, various types of coexisting asymmetric solutions, and period-doubling transition to chaos. We perfectly demonstrate that the new asymmetric/symmetric memristive system exhibits the exciting phenomenon of partial amplitude control (PAC) and offset boosting. Also, we show how it is possible to control the amplitude and the offset of the chaotic signals generated for some technological exploitation. Finally, coexisting solutions (i.e., multistability) found in the novel memristive system are further controlled based on a linear augmentation (LA) scheme. Our numerical findings demonstrated the effectiveness of the control technic through interior crisis, reverse period-doubling scenario, and symmetry restoring crisis. The coupled memristive system remains stable with its unique survived periodic attractor for higher values of the coupling strength.
View
Nonvolatile CMOS Memristor, Reconfigurable Array, and Its Application in Power Load Forecasting
Article
  • Jan 2023
The high cost, low yield, and low stability of nanomaterials significantly hinder the application and development of memristors. To promote the application of memristors, researchers proposed a variety of memristor emulators to simulate memristor functions and apply them in various fields. However, these emulators lack nonvolatile characteristics, limiting their scope of application. This article proposes an innovative nonvolatile memristor circuit based on complementary metal–oxide–semiconductor (CMOS) technology, expanding the horizons of memristor emulators. The proposed memristor is fabricated in a reconfigurable array architecture using the standard CMOS process, allowing the connection between memristors to be altered by configuring the on – off state of switches. Compared to nanomaterial memristors, the CMOS nonvolatile memristor circuit proposed in this article offers advantages of low manufacturing cost and easy mass production, which can promote the application of memristors. The application of the reconfigurable array is further studied by constructing an echo state network for short-term load forecasting in the power system.
View
Memristive Hopfield neural network dynamics with heterogeneous activation functions and its application
Article
  • Jan 2024
  • CHAOS SOLITON FRACT
Activation functions play a crucial in emulating biological neurons within artificial neural networks. However, the exploration of neural networks composed of various activation functions and their associated dynamics have not been noticed yet. This paper proposes a novel method by introducing heterogeneous activation functions into a memristive Hopfield neural network for the first time. The special feature of the proposed model lies not only in its ability to mimic the diversity of brain neurons, providing a more realistic and adaptable frame for artificial neural networks but also in its rich dynamic properties suitable for engineering applications. Theoretical and experimental investigations into the dynamics of the memristive Hopfield neural network are conducted, employing phase portraits, bifurcation diagrams, Lyapunov exponent spectra, 0-1 tests, and bi-parameter dynamic maps. Complex dynamical behaviors, including periodic bursting, chaotic bursting, and chaotic state jump are revealed by the numerical simulations. Furthermore, a hardware implementation of the proposed neural network is designed and validated through circuit simulation software, which is consistent with the numerical simulation and confirms the validity of the proposed model. Finally, an encryption scheme based on the chaotic bursting is also proposed and evaluated. Results demonstrate that the chaotic bursting attractor exhibits excellent randomness, making it well-suited for image encryption applications. The novel exploration of heterogeneous activation neuronal networks in this paper may pave the way for further research in the field of more bionic networks with complex dynamical behaviors and their applications.
View
A robust bit-level image encryption based on Bessel map
Article
  • Feb 2024
  • APPL MATH COMPUT
A chaotic map plays a critical role in image encryption (IME). The map used to generate chaotic sequences should perform high dynamic characteristics. In this study, a new chaotic system depending on the Bessel function, so-called Bessel map, and a novel Bessel map-based IME scheme are proposed for the IME. The Bessel map has three control parameters, which provide superior ergodicity and diversity. Bessel map has also order degree rather than Sine map, which is used as a control parameter boosting the security. The chaotic characteristic of the Bessel map is verified through different reliable measurements such as bifurcation diagram, trajectory phase, Lyapunov exponent (LE), sample entropy (SE), permutation entropy (PE), and 0-1 test. Then, the Bessel map is employed in a new bitwise IME (BIME) scheme based on bit-level permutation and diffusion processes. The Bessel map-based BIME is validated through various simulated cryptanalyses and cyberattacks as well as compared with the state-of-the-art schemes. The achieved results demonstrate that the BIME based on the Bessel map ensures the most secure ciphered images thanks to the excellent randomness and complexity performance.
View
A Universal Variable Extension Method for Designing Multiscroll/Wing Chaotic Systems
Article
  • Aug 2023
  • IEEE T IND ELECTRON
Developing a universal design method to construct different multi-scroll/wing chaotic systems (MS/WCSs) has been challenging. This paper proposes a general design method for MS/WCSs called the universal variable extension method (UVEM). It is a simple but effective approach that generates 1-direction (1- D) and 2-D multi-scroll/wing chaotic attractors. Using any doublescroll/wing chaotic system as the basic system, the UVEM is able to construct different MS/WCSs. Employing Chua’s chaotic system and Lorenz chaotic system as two examples, we construct two MSCSs (including 1-D and 2-D) and two MWCSs (including 1-D and 2- D), respectively. Theoretical analysis and numerical simulation show that the constructed MS/WCSs not only can generate 1-D and 2-D multi-scroll/wing chaotic attractors but also have 1-D and 2-D initial boosting behaviors. This means that the MS/WCSs designed by the UVEM are very sensitive to their initial states, and have better unpredictability and more complex chaotic behaviors. To show the simplicity of UVEM in hardware implementation, we develop a fieldprogrammable gate array (FPGA)-based digital hardware platform to implement the designed MS/WCSs. Finally, a new pseudo-random number generator is proposed to investigate the application of the MS/WCSs. All P-values obtained by the NIST SP800-22 test are larger than 0.01, which indicates that the MS/WCSs designed by UVEM have high randomness.
View
A new 4D Memristor chaotic system: Analysis and implementation
Article
  • Jan 2023
  • INTEGRATION
In this paper, a new chaotic memristor system is developed based on a well-known nonlinear circuit. By replacing the nonlinear positive conductance of Shinriki's circuit with a memristor emulator, the new simple chaotic circuit can reduce the number of active elements and reduce power consumption. An analysis of equilibria and stability, dissipative properties, Lyapunov exponents, Kaplan-Yorke dimensions, and bifurcation diagrams is presented as well as numerical simulation of the new memristor chaotic system. As a final step, the electronic circuit is designed using Multisim software, which is complemented by a physical realization to demonstrate the feasibility of the chaotic system.
View