Article
Mathematics
Amina-Aicha Khennaoui, Adel Ouannas, Shaher Momani, Othman Abdullah Almatroud, Mohammed Mossa Al-Sawalha, Salah Mahmoud Boulaaras, Viet-Thanh Pham
Summary: This study presents the implementation of a new chaotic fractional memristor map with hidden attractors. The system dynamics were analyzed with different fractional orders, revealing rich dynamical behavior.
Article
Mathematics, Interdisciplinary Applications
Ivo Petras
Summary: This paper discusses new oscillator structures that include new elements called memory elements, such as memristors, meminductors, and memcapacitors. These circuits can exhibit oscillations and chaotic behavior, and new mathematical models for fractional-order elements and whole oscillator circuits are proposed.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Interdisciplinary Applications
Akif Akgul, Karthikeyan Rajagopal, Ali Durdu, Muhammed Ali Pala, omer Faruk Boyraz, Mustafa Zahid Yildiz
Summary: In this paper, a novel fractional-order chaotic circuit with a memristor and a memcapacitor with a linear inductor was created. Various dynamical properties of the system were investigated and it was applied to secure communication systems for the first time, showing rich dynamic properties suitable for different engineering applications.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Computer Science, Information Systems
Sara M. Mohamed, Wafaa S. Sayed, Ahmed H. Madian, Ahmed G. Radwan, Lobna A. Said
Summary: This paper extends a memristive chaotic system with transcendental nonlinearities to the fractional-order domain. The chaotic properties of the extended system are validated through bifurcation analysis and spectral entropy. The presented system is employed in the substitution stage of an image encryption algorithm, demonstrating its efficiency through statistical tests, key sensitivity analysis, and resistance to brute force and differential attacks. The proposed system includes reconfigurable coordinate rotation digital computer (CORDIC) and Grunwald-Letnikov (GL) architectures for trigonometric and hyperbolic functions and fractional-order operator implementations, respectively. It achieved a throughput of 0.396 Gbit/s on the Artix-7 FPGA board.
Article
Computer Science, Information Systems
Chuan Qin, Kehui Sun, Shaobo He
Summary: A fractional-order memristive model with infinite coexisting attractors is investigated in this paper. The numerical solution of the system is derived and its dynamic behaviors are analyzed using various methods, showing rich dynamic characteristics including asymmetric coexisting attractors with different structures. The correctness of the solution algorithm and the physical feasibility of the system is verified through digital signal processor (DSP) implementation.
Article
Physics, Multidisciplinary
Weiyang Wang, Guangyi Wang, Jiajie Ying, Gongzhi Liu, Y. A. N. Liang
Summary: This paper proposes a fractional-order locally active memristor based on the definition of fractional derivative. It is found that the side lobe area of the pinched hysteretic curve of the memristor changes with the fractional-order value, and the memory of the fractional-order memristor is stronger than that of the memristor with integer order. The fractional-order memristor possesses continuous memory as proved by the dynamic rout map (DRM). Furthermore, a fractional-order chaotic circuit is constructed using the memristor, which exhibits continuous chaotic motion and various coexisting attractors.
PRAMANA-JOURNAL OF PHYSICS
(2022)
Article
Engineering, Mechanical
Xiaojun Liu, Ling Hong, Dafeng Tang, Lixin Yang
Summary: This paper investigates the boundary and interior crises in a fractional-order piecewise system using the extended generalized cell mapping (EGCM) method. The EGCM method is used to deal with the non-smooth characteristics of the system. It is found that boundary crisis occurs when a chaotic attractor collides with a regular saddle, while interior crisis happens when the chaotic saddle and chaotic attractor touch each other. Additionally, the routes to chaos and out of chaos are explored using the EGCM method.
NONLINEAR DYNAMICS
(2021)
Article
Physics, Multidisciplinary
Najeeb Alam Khan, Muhammad Ali Qureshi, Saeed Akbar, Asmat Ara
Summary: A new five-dimensional fractional-order chaotic system is proposed based on the Lorenz-Stenflo model with a feedback memristor, which exhibits a two-wing attractor with symmetrical coexistence. The system is found to be unstable and hyperchaotic through stability analysis and Lyapunov exponents calculation. Analogue circuits are implemented for both open-loop and closed-loop memristive systems, and the simulation results show good agreement with numerical simulations. Furthermore, a new cryptographic scheme is presented using random data from the chaotic system for multimedia encryption.
Article
Mathematics, Interdisciplinary Applications
Maitreyee Dutta, Binoy Krishna Roy
Summary: This paper introduces a new memductance-based fractional-order chaotic system and demonstrates its characteristics under specific initial conditions. Synchronisation between two identical chaotic systems is achieved through fixed-time convergence technique, showing good robustness against disturbances and parametric uncertainties. Through switching between synchronisation and anti-synchronisation, the algorithm's performance is shown, with simulation results indicating satisfactory performance.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Hongguang Fan, Jiahui Tang, Kaibo Shi, Yi Zhao
Summary: This article addresses the issue of synchronization in fractional-order multi-link memristive neural networks with multiple delays under hybrid impulsive feedback control. Theoretical results are obtained by establishing an extended fractional-order delayed comparison principle and leveraging Laplace transform, Mittag-Leffler functions, the generalized comparison principle, and hybrid impulsive feedback control schemes. The findings contribute to expanding the theoretical achievements of fractional-order neural networks incorporating memristive characteristics.
FRACTAL AND FRACTIONAL
(2023)
Article
Physics, Multidisciplinary
Xiangxin Leng, Limeng Zhang, Chenkai Zhang, Baoxiang Du
Summary: In this paper, a five-dimensional conservative memristor chaotic system is constructed by introducing memristors into a four-dimensional conservative chaotic system. The dynamic changes of the system are analyzed using phase diagrams, mean values, and Lyapunov exponent spectra. The system exhibits characteristics such as line equilibrium points, symmetry, and multi-stability. Furthermore, the complexity of the system increases with the inclusion of memristors and fractional-order differential operators.
Article
Mathematics
Xinggui Li, Ruofeng Rao, Shouming Zhong, Xinsong Yang, Hu Li, Yulin Zhang
Summary: This paper presents a new global Mittag-Leffler synchronization criterion for fractional-order hyper-chaotic financial systems by designing impulsive control and state feedback controller. The significance lies in achieving synchronization between backward and advanced economic systems under effective impulse macroeconomic management means. The effectiveness of the proposed methods is demonstrated in a numerical example, overcoming the mathematical difficulty of non-Lipschitz continuous activation function.
Article
Materials Science, Multidisciplinary
Yuexi Peng, Shaobo He, Kehui Sun
Summary: This paper investigates an interesting second-order memristor-based map model using Caputo fractional-order difference, and explores its dynamic behaviors through various analysis methods. The numerical simulations show that the fractional-order system exhibits a range of complex behaviors, laying a solid foundation for future analysis and engineering applications of discrete memristors.
RESULTS IN PHYSICS
(2021)
Article
Engineering, Multidisciplinary
Babajide Oluwatosin Oresanya, Gangquan Si, Zhang Guo, Xiang Xu, Yiyuan Bie
Summary: This work presents a cubic model of flux-controlled memristor and analyzes its characteristics at various fractional orders, while designing corresponding simulator circuits. The correctness of numerical analysis and calculations is verified through PSPICE simulations, showing that the fractional-order cubic model can induce chaos in Chua's circuit and enhance system dynamics.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Engineering, Electrical & Electronic
Ningning Yang, Ni Liu, Chaojun Wu
Summary: A novel active generalized fractional-order memristor is constructed and its mathematical model is analyzed and verified through theoretical calculation, numerical simulation, and hardware experiment. The circuit exhibits chaotic behavior and the results are consistent with the expected outcomes.
CIRCUITS SYSTEMS AND SIGNAL PROCESSING
(2023)
Article
Mathematics, Applied
Marius -F. Danca
Summary: This paper investigates two important issues regarding the discrete version of Caputo's fractional-order discrete maps defined on the complex plane, namely the attractors' symmetry-breaking induced by the fractional-order derivative and the sensitivity in determining the bifurcation diagram. It is proven that integer-order maps with dihedral symmetry or cycle symmetry may lose their symmetry once they are transformed to fractional-order maps. Furthermore, it is conjectured that determining the bifurcation diagrams of fractional-order maps is far from being well understood, unlike in the case of integer-order maps. Two examples, the dihedral logistic map and cyclic logistic map, are presented for illustration.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Applied
Marius-F. Danca
Summary: In this paper, the parameter switching (PS) algorithm is used to control the dynamics of an autonomous mathematical model of COVID-19. It is shown that every attractor of the system can be numerically approximated using this algorithm, allowing for the determination of stable periodic motion or chaotic attractors. The PS algorithm can be considered as a chaos control or anticontrol algorithm, generating attractors that belong to the system attractor set. It is analytically proven that every system attractor can be expressed as a convex combination of existing attractors using the PS algorithm. Interestingly, the PS algorithm can be viewed as a generalization of Parrondo's paradox.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Computer Science, Artificial Intelligence
Yang Lou, Ruizi Wu, Junli Li, Lin Wang, Chang-Bing Tang, Guanrong Chen
Summary: This study proposes an efficient robustness predictor based on multiple convolutional neural networks (mCNN-RP) for predicting the network connectivity robustness. By classifying and estimating networks, it can accurately predict the connectivity robustness of different complex networks and outperforms existing prediction measures.
Article
Engineering, Mechanical
Marius-F. Danca, Michal Feckan
Summary: In this paper, the fractional-order Mandelbrot and Julia sets in the sense of q-th Caputo-like discrete fractional differences are introduced and their properties are examined analytically and numerically. Surprising properties of the fractional models are discovered, challenging previous expectations. The authors conjecture that the fractional-order Mandelbrot and Julia sets exhibit similarities to the integer-order sets in certain q and c configurations, which is supported by extensive numerical experiments. The algorithms for drawing the sets are presented as pseudocode.
NONLINEAR DYNAMICS
(2023)
Article
Automation & Control Systems
Bing Mao, Xiaoqun Wu, Jinhu Lu, Guanrong Chen
Summary: This article investigates the uniformly predefined-time bounded consensus of leader-following multiagent systems with unknown system nonlinearity and external disturbance. Distributed adaptive fuzzy control is used to analyze and design the system, achieving global consensus within a predefined time.
IEEE TRANSACTIONS ON CYBERNETICS
(2023)
Article
Automation & Control Systems
Jie-Ning Wu, Xiang Li, Guanrong Chen
Summary: This article examines the controllability of multi-input/multi-output linear time-invariant systems in a snapback interlayer coupling framework. It establishes necessary and sufficient conditions for the controllability of three-layer snapback networks and obtains controllability conditions for the superposition of these networks. These conditions are related to smaller scale factor networks and illustrate the impact of interlayer coupling frameworks, intralayer network topologies, node dynamics, inner interactions, and external control inputs on the controllability of snapback networks. The controllability conditions of three-layer snapback networks are also extended to the M-layer setting. Several examples are provided to illustrate the effectiveness of these controllability conditions.
IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS
(2023)
Article
Mathematics
Jiali Wang, Changbing Tang, Jianquan Lu, Guanrong Chen
Summary: In this paper, a decision optimization method based on zero-determinant (ZD) strategies is proposed to help workers in a crowdsourcing system make optimal decisions under incomplete information. The problem is formulated as an iterated game with incomplete information, and the optimal decision of workers in terms of ZD strategies is analyzed. Numerical simulations are conducted to demonstrate the performances of different strategies and the impact of parameters on the payoffs of workers.
Article
Mathematics, Interdisciplinary Applications
Marius-F. Danca, Jagan Mohan Jonnalagadda
Summary: This paper demonstrates that a certain class of discrete Piece Wise Continuous (PWC) systems with Caputo-type delta fractional difference might not have solutions. To overcome this issue, the discontinuous problem is rephrased as a continuous fractional problem. By applying Filippov's theory, the single-valued PWC problem is transformed into a set-valued problem, and then Cellina's theorem enables the restart of the problem as a single-valued continuous one. A numerical example is presented and analyzed.
FRACTAL AND FRACTIONAL
(2023)
Article
Automation & Control Systems
Wenbo Hu, Fei Chen, Linying Xiang, Guanrong Chen
Summary: This article studies coordinated tracking of underactuated and uncertain autonomous surface vehicles (ASVs) via model-reference reinforcement learning control. It is demonstrated that the proposed algorithm has a better performance over baseline control and effectively improves the training efficiency over reinforcement learning.
IEEE TRANSACTIONS ON CYBERNETICS
(2023)
Article
Automation & Control Systems
Zhen Liu, Liangguang Pan, Guanrong Chen
Summary: In this article, a computational model called link-information augmented twin autoencoders is proposed to remove noisy links from observed network and recover the real network. Extensive experiments show that the proposed model outperforms other methods in network denoising and provides interpretable evidence to support its superiority.
IEEE TRANSACTIONS ON CYBERNETICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Yuqian Zhou, Guanrong Chen, Jibin Li
Summary: By applying the techniques from dynamical systems and singular traveling wave theory developed by Li and Chen [2007] to analyze the traveling wave system of the cubic Camassa-Holm type equation, it has been discovered that the bifurcation portraits of this equation exhibit all possible exact explicit bounded solutions (solitary wave solutions, periodic wave solutions, peakon as well as periodic peakons) under different parameter conditions. A total of 19 explicit exact parametric representations of the traveling wave system of the Camassa-Holm type equation are provided.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2023)
Article
Mathematics, Interdisciplinary Applications
Marius-F. Danca
Summary: This paper numerically analyzes the shape of the stability domain Sq for a class of difference systems defined by the Caputo forward difference operator delta(q) of order q is an element of (0,1). The results show that, due to the power of the negative base in the expression of the stability domain, Sq could have additional regions where stability is not verified, in addition to the known cardioid-like shapes. The Mandelbrot map of fractional order is used as an illustrative example, and it is conjectured that for q < 0.5, the shape of Sq does not cover the main body of the underlying Mandelbrot set of fractional order as in the case of integer order.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Michal Feckan, Marius-F. Danca
Summary: In this paper, we examine the non-periodicity of a certain class of complex maps defined in the sense of Caputo-like fractional differences, as well as the asymptotical stability of fixed points. The Mandelbrot map of fractional order is taken as an example.
FRACTAL AND FRACTIONAL
(2023)
Article
Computer Science, Artificial Intelligence
Jiajun Zhou, Zhi Chen, Min Du, Lihong Chen, Shanqing Yu, Guanrong Chen, Qi Xuan
Summary: In this paper, robust community detection methods are proposed to improve the performance and robustness of community detection for real-world networks. By enhancing network structure through two generic algorithms, significant performance improvement is achieved for representative community detection algorithms. Additionally, the new methods also optimize the network structure and enhance robustness against adversarial attack.
IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING
(2023)
Article
Mathematics, Applied
Zhensu Wen, Guanrong Chen
Summary: This paper uses the methodology of dynamical systems and singular traveling wave theory to prove the existence of all possible bounded solutions of the traveling wave system in the Hertz chain model under different parameter conditions. Furthermore, it obtains 23 exact explicit parametric representations for various types of traveling wave systems.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2023)
Article
Mathematics, Interdisciplinary Applications
Bo Li, Tian Huang
Summary: This paper proposes an approximate optimal strategy based on a piecewise parameterization and optimization (PPAO) method for solving optimization problems in stochastic control systems. The method obtains a piecewise parameter control by solving first-order differential equations, which simplifies the control form and ensures a small model error.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Guram Mikaberidze, Sayantan Nag Chowdhury, Alan Hastings, Raissa M. D'Souza
Summary: This study explores the collective behavior of interacting entities, focusing on the co-evolution of diverse mobile agents in a heterogeneous environment network. Increasing agent density, introducing heterogeneity, and designing the network structure intelligently can promote agent cohesion.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Gengxiang Wang, Yang Liu, Caishan Liu
Summary: This investigation studies the impact behavior of a contact body in a fluidic environment. A dissipated coefficient is introduced to describe the energy dissipation caused by hydrodynamic forces. A new fluid damping factor is derived to depict the coupling between liquid and solid, as well as the coupling between solid and solid. A new coefficient of restitution (CoR) is proposed to determine the actual physical impact. A new contact force model with a fluid damping factor tailored for immersed collision events is proposed.
CHAOS SOLITONS & FRACTALS
(2024)
