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Symmetry
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Discrete and Continuous Memristive Nonlinear Systems and Symmetry II
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Discrete and Continuous Memristive Nonlinear Systems and Symmetry II

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: 31 October 2024 | Viewed by 3356

Special Issue Editors

Dr. Shaobo He

E-Mail Website
Guest Editor
School of Physics and Electronics, Central South University, Changsha 410083, China
Interests: complex dynamic properties of nonlinear systems; memristor and memristor neural networks; complex networks; fractional calculus and its applications
Special Issues, Collections and Topics in MDPI journals
Dr. Quan Xu

E-Mail Website
Guest Editor
School of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, China
Interests: memristive circuit/system; memristive neuromorphic circuit; bifurcation analysis; neuron dynamics
Prof. Dr. Chunlai Li

E-Mail Website
Guest Editor
1. School of Computer Science & School of Cyberspace Science, Xiangtan University, Xiangtan 411105, China
2. College of Physics and Electronics, Hunan Institute of Science and Technology, Yueyang 414006, China
Interests: nonlinear circuit; memristor and memristor circuit; memristor neural network; information security

Special Issue Information

Dear Colleagues,

Due to the characteristics of memory and intrinsic nonlinearity, memristors have broad application prospects in fields such as flash memory, logic circuits, synapses, neural networks, and oscillator circuits. Among these, memristor-based applications have been intensively investigated, such as discrete and continuous memristive chaotic systems, memristive neural systems, and memristive nonlinear networks. Meanwhile, fractional calculus is a 300-year-old topic, and now, it has been introduced to different nonlinear systems. Moreover, applications of fractional-order calculus have aroused much interest. As a result, fractional-order discrete and continuous memristors, as well as fractional-order memristor nonlinear systems, have been designed. As a result, symmetry coexisting attractors are found in those systems. For this Special Issue, we focus on discrete and continuous memristive nonlinear systems with or without fractional calculus and their applications, such as nonlinear systems, neural networks, brain-like computing, information encryption, and symmetry. All related work is sincerely welcome.

Dr. Shaobo He
Dr. Quan Xu
Prof. Dr. Chunlai Li
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • chaos
  • nonlinear system
  • memristive system
  • fraction-order memristor
  • fractional-order memristive system
  • image encryption
  • neural network
  • brain-like computing
  • memristor based artificial intelligence
  • symmetry

Published Papers (3 papers)

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Research

14 pages, 2861 KiB  
Article
A Class of Discrete Memristor Chaotic Maps Based on the Internal Perturbation
by Worke Adugna Yihyis, Shaobo He, Zhouqing Tang and Huihai Wang
Symmetry 2023, 15(8), 1574; https://doi.org/10.3390/sym15081574 - 12 Aug 2023
Cited by 1 | Viewed by 669
Abstract
Further exploration into the influence of a memristor on the behavior of chaotic systems deserves attention. When constructing memristor chaotic systems, it is commonly believed that increasing the number of memristors will lead to better system performance. This paper proposes a class of [...] Read more.
Further exploration into the influence of a memristor on the behavior of chaotic systems deserves attention. When constructing memristor chaotic systems, it is commonly believed that increasing the number of memristors will lead to better system performance. This paper proposes a class of chaotic maps with different discrete memristors, achieved through internal perturbation based on the Sine map. The I-V curve of the discrete memristor has a symmetrical structure. The dynamic characteristics of the designed system are analyzed using the chaotic attractor phase diagram, Lyapunov exponent (LE) spectrum, and bifurcation diagram. Numerical simulations demonstrate that internal perturbations of discrete memristors enhance the Sine map’s chaotic characteristics, expand the chaos range, and improve the ergodicity and LE value. Moreover, the type of discrete memristors has a significant impact on the dynamic characteristics of the system, while the number of discrete memristors has little influence. Therefore, in this paper, a direction for the design of a discrete memristor chaotic system is provided. Finally, a discrete memristor chaotic map with a simple structure and better performance is selected. Based on this, a pseudo-random sequence generator is designed, and the generated sequence passes the National Institute of Standards and Technology (NIST) test. Full article
(This article belongs to the Special Issue Discrete and Continuous Memristive Nonlinear Systems and Symmetry II)
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31 pages, 18830 KiB  
Article
A Novel Fractional-Order Memristive Chaotic Circuit with Coexisting Double-Layout Four-Scroll Attractors and Its Application in Visually Meaningful Image Encryption
by Yuebo Wu, Duansong Wang, Tan Zhang, Jinzhong Zhang and Jian Zhou
Symmetry 2023, 15(7), 1398; https://doi.org/10.3390/sym15071398 - 11 Jul 2023
Viewed by 1101
Abstract
This paper proposes a fractional-order chaotic system using a tri-stable locally active memristor. The characteristics of the memristor, dynamic mechanism of oscillation, and behaviors of the proposed system were analyzed, and then a visually meaningful image encryption scheme was designed based on the [...] Read more.
This paper proposes a fractional-order chaotic system using a tri-stable locally active memristor. The characteristics of the memristor, dynamic mechanism of oscillation, and behaviors of the proposed system were analyzed, and then a visually meaningful image encryption scheme was designed based on the chaotic system, DNA encoding, and integer wavelet transform (IWT). Firstly, the mathematical model of the memristor was designed, which was nonvolatile, locally active, and tri-stable. Secondly, the stability, dynamic mechanism of oscillation, bifurcation behaviors, and complexity of the fractional-order memristive chaotic system were investigated and the conditions of stability were obtained. Thirdly, the largest Lyapunov exponent, bifurcation diagram, and complexity of the novel system were calculated and the coexisting bifurcation, coexisting attractors, spectral entropy, and so on are shown. Finally, a visually meaningful image encryption scheme based on the proposed system was designed, and its security was assessed by statistical analysis and different attacks. Numerical simulation demonstrated the effectiveness of the theoretical analysis and high security of the proposed image encryption scheme. Full article
(This article belongs to the Special Issue Discrete and Continuous Memristive Nonlinear Systems and Symmetry II)
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13 pages, 2868 KiB  
Article
A New Pelican Optimization Algorithm for the Parameter Identification of Memristive Chaotic System
by Qi Xiong, Jincheng She and Jinkun Xiong
Symmetry 2023, 15(6), 1279; https://doi.org/10.3390/sym15061279 - 19 Jun 2023
Cited by 3 | Viewed by 1074
Abstract
A memristor is a kind of nonlinear electronic component. Parameter identification for memristive chaotic systems is a multi-dimensional variable optimization problem. It is one of the key issues in chaotic control and synchronization. To identify the unknown parameters accurately and quickly, we introduce, [...] Read more.
A memristor is a kind of nonlinear electronic component. Parameter identification for memristive chaotic systems is a multi-dimensional variable optimization problem. It is one of the key issues in chaotic control and synchronization. To identify the unknown parameters accurately and quickly, we introduce, in this paper, a modified Pelican Optimization Algorithm (POA) called the fractional-order chaotic Pareto Pelican Optimization Algorithm (FPPOA). First, the pelican population’s diversity is augmented with the integration of a fractional chaotic sequence. Next, the utilization of the Pareto distribution is incorporated to alter the hunting strategy of pelicans in the POA. These measures are effective in hastening the speed of finding an optimal solution and circumventing local optimization issues. Thirdly, the FPPOA is used to determine the values of the parameters of the simplest memristive chaotic system, which has a property of conditional symmetry. The proposed algorithm was evaluated during simulations, where it was utilized to solve six objective functions of varying unimodal and multimodal types. The performance of the FPPOA exceeds three traditional swarm intelligence optimization algorithms. In the parameter identification experiment, the results for the parameters with the FPPOA had error rates all within a 1% range. Extensive testing shows that our new strategy has a faster rate of convergence and better optimization performance than some other traditional swarm algorithms. Full article
(This article belongs to the Special Issue Discrete and Continuous Memristive Nonlinear Systems and Symmetry II)
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