Article
Multidisciplinary Sciences
Susan Razmara, Meisam Yahyazadeh
Summary: In this study, a comprehensive robust control approach is proposed for the projective synchronization of chaotic systems. The approach considers dissimilar structures, mismatched time delays, non-identical fractional derivative orders, uncertainties, and external disturbances. Based on fractional-order sliding mode control strategy and fractional-order Lyapunov stability theorem, the synchronized systems are utilized to design an analog time-varying audio cryptography system. Numerical simulations and security analysis demonstrate that the designed audio cryptography system has more accurate and secure results and easier practical implementation than previous systems.
ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING
(2022)
Article
Multidisciplinary Sciences
A. E. Matouk
Summary: Studying chaotic dynamics in fractional-and integer-order dynamical systems has helped researchers understand and predict the mechanisms of related non-linear phenomena. This paper reports the existence of chaotic attractors that exist only in the fractional-order case when using the specific selection of parameter values in a new hyperchaotic (Matouk's) system.
JOURNAL OF ADVANCED RESEARCH
(2023)
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
Automation & Control Systems
Jia Jia, Zhigang Zeng, Fei Wang
Summary: This paper investigates global asymptotical synchronization of fractional-order memristor-based neural networks with multiple time-varying delays using pinning control. Two classes of coupling manners, static and dynamic, are introduced. Different methods and inequalities are utilized for synthesis of controller and analysis of synchronization error in static and dynamic coupling cases.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Fei Qi, Jianfeng Qu, Yi Chai, Liping Chen, Antonio M. Lopes
Summary: This paper investigates the synchronization of incommensurate fractional-order (FO) chaotic systems and proposes a sufficient condition for achieving synchronization using linear matrix inequalities (LMIs). The effectiveness and feasibility of the method are demonstrated through examples involving two typical FO chaotic systems.
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
Physics, Multidisciplinary
D. Vignesh, Naa Fataf, M. F. Abdul Rahim
Summary: This article proposes a fractional order discrete-time neuromuscular model and conducts dynamic analysis, synchronization control, and chemical interpretation to reveal the essential role of the neuromuscular system in information transmission and disease control.
Article
Physics, Multidisciplinary
Lilian Huang, Wenya Li, Jianhong Xiang, Genglei Zhu
Summary: In this paper, a finite-time adaptive synchronization method based on sliding-mode control is introduced to achieve the generalized projective synchronization of fractional-order memristor chaotic systems with unknown parameters. By designing a new fractional-order integral sliding-mode surface, a controller with adjustable parameters, and adaptive laws, the synchronization error system can reach the sliding-mode surface in finite time and the unknown parameters can be identified. Numerical simulations demonstrate the effectiveness of the proposed synchronization strategy in achieving generalized projection synchronization and unknown parameter identification of fractional-order memristor chaotic systems in a short time.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2022)
Article
Physics, Multidisciplinary
Xiaojun Liu, Dafeng Tang, Ling Hong
Summary: In this paper, a novel fractional-order discrete map with typical nonlinear features, such as chaos and bifurcations, is proposed. The stability and symmetry of the map are analyzed by theoretical analysis. The dynamics and bifurcation types of the map are investigated through numerical simulations. The hybrid synchronization of the map is achieved by designing suitable controllers.
Article
Physics, Mathematical
Yanyun Xie
Summary: In this paper, a discrete Lorenz map with fractional difference is analyzed, and the bifurcations of the map in different cases are studied. The relationship between the parameter values and the order of the bifurcation points is determined. Additionally, chaos control and synchronization for the fractional-order discrete Lorenz map are investigated through designing suitable controllers.
ADVANCES IN MATHEMATICAL PHYSICS
(2022)
Article
Physics, Applied
Ningning Yang, Shuo Yang, Chaojun Wu
Summary: In this paper, a novel four-dimensional fractional-order chaotic system is proposed and its dynamic characteristics are analyzed. The system's electronic circuit is designed and implemented using PSpice. The system is also implemented using FPGA. The synchronization of two systems with different initial values is realized by finite time control method and FPGA.
MODERN PHYSICS LETTERS B
(2022)
Article
Physics, Multidisciplinary
Yuxi Li, Zhouchao Wei, Ayman A. Aly
Summary: This paper studies the complex dynamics of a newly proposed 4D hyperchaotic Lorenz-type system. The sufficient conditions for the emergence of periodic solutions and their stability at bifurcation points are obtained using averaging theory. The ultimate bound estimation of this hyperchaotic system is derived using Lyapunov stability theory and optimization idea, and relevant numerical simulations are provided. Finally, a variable-order fractional network of this new 4D hyperchaotic Lorenz-type system is introduced and investigated.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2022)
Article
Mathematics, Interdisciplinary Applications
M. Higazy, George Maria Selvam, R. Janagaraj
Summary: This paper analyzes the chaotic dynamics of a novel 2D fractional order discrete Ushiki map using Caputo-like delta fractional difference operator. The proposed theoretical findings are validated through numerical examples.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2021)
Article
Mathematics
Dongya Li, Xiaoping Zhang, Shuang Wang, Fengxiang You
Summary: This paper investigates the synchronization problem for a class of chaotic systems subjected to disturbances. A feedback law is designed to achieve H∞ performance, and a detailed algorithm for computing the incremental multiplier matrix is provided. The effectiveness of the proposed method is demonstrated through numerical and practical examples.
Article
Engineering, Mechanical
Haoyu Zhang, Kehui Sun, Shaobo He
Summary: This study introduces Caputo fractional-order definition into a ship power system, constructing a system with extreme multistability. The dynamics of the system are analyzed using phase diagrams, bifurcation diagrams, Lyapunov exponents, and SE complexity, revealing rich dynamical characteristics.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Applied
P. Balasubramaniam
Summary: This paper discusses the existence result for a class of non-instantaneous impulsive Hilfer fractional stochastic systems driven by mixed Brownian motion and Levy noise. Sufficient conditions for the existence of solutions are obtained by utilizing mathematical tools and methods, and an example is provided for illustration.
STOCHASTIC ANALYSIS AND APPLICATIONS
(2023)
Article
Computer Science, Information Systems
P. Muthukumar, Nasreen Khan
Summary: This paper presents a study on the dynamical properties of a new fractional-order real hyper-chaotic system and its corresponding complex variable system. The analysis involves evaluating the effects of varying fractional-order derivative and parameter values on the system through stability of equilibrium points, phase plots, Lyapunov spectrum, and bifurcation analysis. A modulus synchronization scheme is proposed for the first time to synchronize real and complex fractional-order dynamical systems. Non-linear controllers are designed based on Lyapunov stability theory to achieve the proposed modulus synchronization scheme. Additionally, a new modulus synchronization encryption algorithm with a large key space size for digital images is introduced and validated through experimental results and analysis, showing its efficacy compared to previous literature. Numerical simulations are provided to validate the theoretical analysis.
MULTIMEDIA TOOLS AND APPLICATIONS
(2023)
Article
Computer Science, Artificial Intelligence
R. Vijay Aravind, P. Balasubramaniam
Summary: This article presents a fuzzy sampled-data controller for nonlinear semi-Markovian jump systems (SMJS) using the fuzzy dependent stochastic looped-Lyapunov functional (FSLF) approach. The stochastic jump parameters, actuator faults, and logarithmic quantizer are considered within a unified framework using the Takagi-Sugeno (T-S) method. The proposed controller scheme ensures stochastic stability for the nonlinear SMJS in the presence of actuator faults and state quantization.
IEEE TRANSACTIONS ON FUZZY SYSTEMS
(2023)
Article
Automation & Control Systems
N. Ramesh Babu, P. Balasubramaniam
Summary: This paper investigates the synchronization problem of stochastic quaternion-valued neural networks (SQVNNs) with mixed time-varying delays. A linear feedback controller is developed to achieve global synchronization by utilizing complete information of the time-delay state. Sufficient conditions for synchronization are derived by constructing appropriate Lyapunov-Krasovskii functional using the master-slave synchronization method and integral inequality techniques. Numerical simulation confirms the accuracy of the theoretical results. Additionally, the paper introduces a unique image encryption algorithm based on SQVNNs, which generates high-level randomness secret keys for encrypting source images. The algorithm demonstrates excellent diffusion and confusion properties, providing an efficient and secure solution for the Internet of Health Things (IoHT).
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2023)
Article
Computer Science, Interdisciplinary Applications
N. Ramesh Babu, P. Balasubramaniam
Summary: This study focuses on a new model of diabetes metabolism by incorporating food intake as a disturbance to simulate type-1 diabetes. It introduces a new fractional operator and power law convolution to analyze the characteristics. The theoretical results are verified through numerical simulations.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Mathematics, Applied
K. Dhanalakshmi, P. Balasubramaniam
Summary: This manuscript addresses the existence and exponential stability of impulsive fractional neutral stochastic integrodifferential equations (IFNSIDEs) driven by Poisson jump and fractional Brownian motion (fBm) with nonlocal conditions via the Winch fixed point theorem. The sufficient conditions for stability results are derived based on the pth moment exponential stable with the help of new impulsive integral inequality. Finally, a numerical example is presented to illustrate the efficiency of the theoretical results with different Hurst index H in ((1)/(2), 1).
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES
(2023)
Article
Mathematics, Applied
R. Vijay Aravind, P. Balasubramaniam
Summary: This paper investigates the ML stability analysis problem of memristor-based fractional-order Cohen-Grossberg neural networks with time delays and uncertainties. Sufficient conditions are derived based on fractional-order Lyapunov direct approach and differential inclusion theory, and expressed in terms of linear matrix inequalities. The validity and efficacy of the obtained theoretical results are demonstrated by numerical example and simulation results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Physics, Mathematical
K. Dhanalakshmi, P. Balasubramaniam
Summary: In this paper, sufficient conditions are established for the Ulam-Hyers stability of second-order non-instantaneous impulsive fractional neutral stochastic differential equations (NIIFNSDEs) with supremum norm in the pth means square sense. The existence of solution of NIIFNSDEs is derived by using the cosine family of linear operator, Ito's formula, and Mo and #776;nch fixed point theorem in infinite-dimensional space. Finally, an example is demonstrated to illustrate the obtained theoretical results.
JOURNAL OF MATHEMATICAL PHYSICS
(2023)
Article
Computer Science, Artificial Intelligence
M. Rakshana, P. Balasubramaniam
Summary: This paper considers a fractional model of a special structure of bidirectional associative memory (BAM) neural networks called tri-diagonal BAM neural networks (TdBAMNNs). Hopf bifurcation analysis is performed for the proposed fractional system in the presence of leakage and communication delays. The feasibility of the obtained theoretical results is verified through numerical simulations.
NEURAL PROCESSING LETTERS
(2023)
Article
Automation & Control Systems
C. Mattuvarkuzhali, P. Balasubramaniam, M. J. Er
Summary: This paper develops a nonlinear mathematical model to deal with the exponential stability of visual trajectory in the I-cub robot. The main contributions are: 1) studying exponential stability for neutral fractional stochastic differential equations (NFSDEs) driven by mixed Brownian motion (Bm) and subfractional Bm (sub-fBm) for the first time in the literature; 2) deriving existence and stability results based on the Banach contraction principle, semi-group theory, and fractional calculus in stochastic settings; 3) establishing stability results of mixed Bm and sub-fBm and applying them to avoid stochastic disturbance in the visual trajectory of the I-cub robot in dense environments; and 4) ensuring stability of sub-fBm even in small particles from the shorter length in dense environments. The obtained results are new and innovative, and have several advantages for gaze shift and high-quality visual tracking in the I-cub robot.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)
Article
Mathematics, Applied
K. Sanjay, R. Vijay Aravind, P. Balasubramaniam
Summary: This article addresses the problem of extended dissipative filtering design for the class of nonlinear interconnected systems with time-varying delays under the cyber attacks. The proposed interconnected systems (ISs) are modeled using the Takagi-Sugeno fuzzy (TSF) IF-THEN rules. The filter design takes into account the sensor delays and the influence of cyber attacks for more practicality.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Computer Science, Artificial Intelligence
J. Reegan Jebadass, P. Balasubramaniam
Summary: Image fusion is a technique for improving image quality by extracting critical information. The proposed method based on intuitionistic fuzzy sets converts given images into fuzzy images and then into interval type-2 fuzzy images, achieving the best visual quality and performance evaluation results.
APPLIED SOFT COMPUTING
(2023)
Article
Computer Science, Artificial Intelligence
R. Vijay Aravind, P. Balasubramaniam
Summary: This article investigates the fuzzy sampled-data control problem for switched nonlinear systems. By introducing a new fuzzy dependent refined looped Lyapunov functional and considering the AE-DADT switching property, sufficient conditions for global uniform exponential stability of the switched IT2F systems are derived.
IEEE TRANSACTIONS ON FUZZY SYSTEMS
(2023)
Article
Computer Science, Information Systems
N. Ramesh Babu, P. Balasubramaniam, Er. Meng Joo
Summary: In this paper, a mathematical modeling of a fractional-order memristor circuit is developed by using fractional elements instead of classical circuit elements. The main contributions of this research include remodelation of a fractional order non-linear memristive hyper-chaotic system, synchronization of sender and receiver system with video cryptosystem applications, design of a fuzzy feedback controller for synchronization of the hyperchaotic system, development of video encryption and decryption algorithms, analysis of various metrics for high-level security, and demonstration of the effectiveness of the proposed algorithms through numerical simulations and experimental results.
MULTIMEDIA TOOLS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
K. Dhanalakshmi, P. Balasubramaniam
Summary: In this manuscript, the authors establish the existence, uniqueness, and stability results for the second-order non-instantaneous impulsive fractional neutral stochastic differential equations (NIIFNSDEs). They use Caputo fractional derivative, stochastic technique, and fixed point approach with appropriate assumptions on nonlinear continuous functions to obtain the existence and uniqueness results. They also study the Ulam-Hyers Rassias stability and provide an example to validate the theoretical findings.
BULLETIN DES SCIENCES MATHEMATIQUES
(2023)
