Article
Mathematics, Applied
D. Vignesh, Shaobo He, Santo Banerjee
Summary: This article introduces a discrete time fractional order three-dimensional Rucklidge system with complex state variables and compares its dynamical properties and chaotic behavior with the Rucklidge system with real state variables and higher dimensional system derived from complex state variables. The stability of the proposed system is analyzed at equilibrium states by obtaining eigenvalues numerically. Chaotic dynamics exhibited by the system with real and complex variables are studied using bifurcation analysis, maximum Lyapunov exponents, and the Jacobian matrix method. Nonlinear controllers are implemented for chaos synchronization of the subsystems of the proposed system. The article also discusses the coexisting behavior of the attractors in the Rucklidge system with real state variables and coexisting bifurcation diagrams.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Engineering, Multidisciplinary
Samir Bendoukha
Summary: In this paper, a fractional Caputo-difference map based on the 2D generalized Henon map is proposed and studied. Numerical methods, phase plots, and bifurcation diagrams are used to investigate the dynamics of the map. A 1D synchronization controller is proposed and the stability theory of fractional discrete systems is utilized to guarantee the asymptotic convergence of the controller.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Interdisciplinary Applications
Li Ziyan, Tao Ke, Xia Qing, Xie Chengrong, Xu Yuhua
Summary: This study proposes a financial risk dynamic system and uses a finite-time impulse controller to control the risk, which has a faster convergence speed.
Article
Physics, Multidisciplinary
Lu Lu, Chengdai Huang, Xinyu Song
Summary: A fractional-order proportional-derivative controller is used to control the bifurcation of a delayed fractional-order prey-predator system. The proper equation of the proposed system is investigated and stability conditions of the equilibrium and critical values of Hopf bifurcation are obtained. The results show the successful deferment of Hopf bifurcation by the proposed controller through proper parameter setting. The correlation between the Hopf bifurcation point and the fractional order is also illustrated. A numeric example is conducted to verify the main results.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Mathematics, Interdisciplinary Applications
Muhammad Fiaz, Muhammad Aqeel, Muhammad Marwan, Muhammad Sabir
Summary: In this article, a 3D autonomous system derived from multiple chaotic systems is studied to verify the existence of zero Hopf bifurcation. Fractional order analysis is conducted to examine stability, chaotification condition, and other properties of the derived system. The synchronization of the derived system with the famous Lorenz model is investigated, and the results are compared using different numerical techniques. The study concludes that if integer order chaotic systems are synchronized, their fractional order versions will also be synchronized for the same parametric values and initial conditions, and vice versa.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Physics, Multidisciplinary
Ahmad Taher Azar, Fernando E. Serrano, Quanmin Zhu, Maamar Bettayeb, Giuseppe Fusco, Jing Na, Weicun Zhang, Nashwa Ahmad Kamal
Summary: This paper presents the robust stabilization and synchronization of a novel chaotic system, including bifurcation analysis and robust controller design. By implementing a sigmoidal function to create chaotic behavior and using robust control Lyapunov function for synchronization, stability is achieved through the control law designed for stabilization and synchronization purposes.
Article
Multidisciplinary Sciences
A. Q. Khan, S. Khaliq, O. Tunc, A. Khaliq, M. B. Javaid, I Ahmed
Summary: This paper investigates the local dynamic characteristics of fixed points with different topological classifications in the discrete Kolmogorov model, exploring the existence of various types of fixed points using algebraic techniques and examining the occurrence of bifurcations. Numerical simulations are used to verify theoretical results and discover new dynamics in the model.
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE
(2021)
Article
Engineering, Mechanical
D. Vignesh, Santo Banerjee
Summary: This article investigates the chaotic behavior of the 2-D vocal dynamical system using commensurate and incommensurate fractional order Caputo difference operator. The analysis shows that the behavior of the system changes with different fractional orders, highlighting the importance of employing incommensurate order models in real-life modeling.
NONLINEAR DYNAMICS
(2023)
Article
Mechanics
Ghasem Arian, Sajjad Taghvaei
Summary: This study analyzes chaotic dynamics and develops a chaos controller for spur gear transmission systems with idler gears. The study establishes a nonlinear time-varying dynamic model, finds a region of chaos occurrence, and suppresses chaotic vibrations through control laws. Numerical simulations confirm the controller's performance.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2021)
Article
Mathematics
Muhamad Deni Johansyah, Aceng Sambas, Saleh Mobayen, Behrouz Vaseghi, Saad Fawzi Al-Azzawi, Ibrahim Mohammed Sulaiman
Summary: This work focused on the complex behaviors of a fractional-order financial chaotic system and enriched the results presented in a previous study. The study analyzed the dynamical behaviors and stability of the system and confirmed its stability under typical parameters. MATLAB simulations were used to characterize the system's properties.
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
Mathematics, Interdisciplinary Applications
Qiaoling Chen, Zhidong Teng, Feng Wang
Summary: This paper explores a two-dimensional discrete-time mosquito model, demonstrating a series of bifurcations of codimension two, such as fold flip and strong resonance bifurcations, as the parameter values change. Theoretical analyses are validated and chaotic behaviors of the model are confirmed through various charts and diagrams.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Xiaohua Ren, Changcheng Xiang, Yi Yang
Summary: This paper investigates the effects of random perturbations on interacting populations and proposes a discrete-time model with biological control. The results show that random perturbations change the number of blurred orbits of the system, enhancing its stability.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
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
Abderrahmane Abbes, Adel Ouannas, Nabil Shawagfeh
Summary: This study proposes a novel fractional discrete-time macroeconomic system with incommensurate order and investigates its dynamical behavior analytically and numerically. The results show that the system exhibits chaotic behavior, which is verified through bifurcation diagrams, phase attractors, the maximum Lyapunov exponent, the 0-1 test, approximation entropy (ApEn), and C (0) complexity analyses. Finally, numerical simulations are used to present the main findings of this study.
Article
Engineering, Aerospace
Fawaz W. Alsaade, Hadi Jahanshahi, Qijia Yao, Mohammed S. Al-zahrani, Ali S. Alzahrani
Summary: This paper proposes a new neural network-based optimal mixed H2=H1 control method for trajectory tracking missions of a modified unmanned aerial vehicle. The control technique aims to predict uncertain dynamics and minimize control energy consumption, considering input constraints and external disturbances. Numerical simulations demonstrate the efficient performance of the proposed method.
ADVANCES IN SPACE RESEARCH
(2023)
Article
Acoustics
Qamar Din
Summary: This study investigates the cyclic types of ecological dynamics in forest Lepidoptera species and explores the interactions with consumers and plant quality index. The results show the existence of flip bifurcation and Hopf bifurcation in the model and introduce methods to control chaos.
JOURNAL OF VIBRATION AND CONTROL
(2023)
Article
Engineering, Aerospace
Hadi Jahanshahi, Qijia Yao, Muhammad Ijaz Khan, Irene Moroz
Summary: A unified neural control scheme is developed for output-constrained trajectory tracking of space manipulator under unknown parameters and external perturbations. The proposed controller integrates backstepping control, neural network, and tan-type barrier Lyapunov function. The neural network is utilized for identifying the unknown part in the dynamic model, making the controller model-free and robust to external disturbances. The tan-type barrier Lyapunov function ensures that position tracking errors do not exceed predefined constraints. The closed-loop system achieves semiglobal uniform ultimate boundedness, and all error variables eventually stabilize around zero. Simulations and comparisons verify the effectiveness and tracking performance of the proposed control scheme.
ADVANCES IN SPACE RESEARCH
(2023)
Article
Multidisciplinary Sciences
Amina-Aicha Khennaoui, Adel Ouannas, Stelios Bekiros, Ayman A. Aly, Ahmed Alotaibi, Hadi Jahanshahi, Hajid Alsubaie
Summary: Fractional order maps have attracted much attention due to their potential applications in various fields. In this paper, a new class of 2D fractional hyperchaotic map is introduced using the Caputo-like difference operator. The system dynamics are analyzed through bifurcation diagrams, Lyapunov exponents, and phase portraits for different fractional orders. The results demonstrate rich dynamical behavior, including hidden homogeneous multistability and offset boosting.
Article
Mathematics, Interdisciplinary Applications
M. I. N. G. Z. H. U. Tang, C. A. I. H. U. A. Meng, L. A. N. G. LI, H. U. A. W. E. Wu, Y. A. N. G. Wang, J. U. N. B. I. N. He, Y. U. J. I. E. Huang, Y. U. Yu, M. A. D. I. N. I. O. Alassafi, F. A. W. A. Z. E. Alsaadi, A. D. I. L. M. Ahmad, F. U. Q. I. A. N. G. Xiong
Summary: An improved Borderline-SMOTE oversampling method called TSDAS-SMOTE is proposed to address the class-imbalance issue in wind turbine pitch connecting bolt data. TSDAS-SMOTE, combined with XGBoost, is used to construct a fault detection model. Experimental results show that the proposed method outperforms six popular oversampling methods in terms of missed alarm rate (MAR) and false alarm rate (FAR), achieving effective fault detection for large wind turbine pitch connection bolts.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Mathematics, Interdisciplinary Applications
Xue Tian, Madini O. Alassafi, Fawaz E. Alsaadi
Summary: The cultivation of creativity is closely related to language learning, and the challenge faced by English teachers is how to design the creativity promotion mechanism of English teaching in the public environment. With the advent of the era of big data, English teachers can apply the latest research results to classroom teaching, using social media to help students learn and communicate in the language, cultivate their creativity in learning English, and improve the quality of teaching.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Mathematics, Interdisciplinary Applications
Mingzhu Tang, Jun Tang, Huawei Wu, Yang Wang, Yiyun Hu, Beiyuan Liu, Madini O. Alassafi, Fawaz E. Alsaadi, Adil M. Ahmad, Fuqiang Xiong
Summary: Abnormal detection of wind turbine converter is a crucial technology for ensuring the stable operation and safe power generation of wind turbines. To address the issue of limited abnormal data and low recognition rate, a sample enhancement method based on an improved conditional Wasserstein generative adversarial network is proposed. Experimental results demonstrate that this method achieves lower MAR and FAR in the anomaly detection of wind turbine converters, outperforming other oversampling data balance optimization methods such as SMOTE, RandomOverSampler, GAN, etc.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Computer Science, Information Systems
Xiaoyang Chen, Jun Mou, Yinghong Cao, Huizhen Yan, Hadi Jahanshahi
Summary: This paper proposes two hyperchaotic systems and new DNA operation rules for image encryption, thereby increasing the complexity of the encryption scheme. The security performance of the proposed algorithm is analyzed in detail by comparing it with traditional Arnold algorithm, histogram, key space, correlation, information entropy, differential attack, and robustness. The experimental results show that the scheme has good performance and improves the security of image encryption and transmission.
MULTIMEDIA TOOLS AND APPLICATIONS
(2023)
Article
Mathematics, Interdisciplinary Applications
Fawaz W. Alsaade, Hadi Jahanshahi, Qijia Yao, Mohammed S. Al-zahrani, Ali S. Alzahrani
Summary: In this paper, a new data-driven-based fractional-order control technique is proposed to address the issue of enabling UAVs to track desired trajectories in challenging environments. The control approach combines a deep neural network with a robust fractional-order controller to estimate uncertainties and minimize the impact of unknown disturbances.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Fawaz W. Alsaade, Mohammed S. Al-zahrani, Qijia Yao, Hadi Jahanshahi
Summary: This study proposes a model-free and finite-time super-twisting control technique for a variable-order fractional Hopfield-like neural network, which can effectively regulate the system's complex dynamic. The dynamics of the variable-order fractional Hopfield-like neural network are examined, the control design is described, and its finite-time stability is proven. The performance of the controller is evaluated under two different scenarios through simulations, and the results demonstrate its excellent performance.
FRACTAL AND FRACTIONAL
(2023)
Article
Engineering, Electrical & Electronic
Yiheng Wei, Linlin Zhao, Junguo Lu, Fawaz E. Alsaadi, Jinde Cao
Summary: This study systematically explores the stability of delta delay fractional order systems with an extra order, addresses the approximation of stable region and the derivation of relevant LMI conditions caused by the complicated stable region. The proposed stability conditions are formulated in terms of LMIs and the validity and applicability of the approaches are demonstrated by simulation study.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
(2023)
Article
Computer Science, Hardware & Architecture
Yuwen Sha, Bo Sun, Hadi Jahanshahi, Linian Wang
Summary: In this paper, a fast and effective chaos-based image cryptosystem is proposed by introducing a dynamical state variables selection mechanism and (7, 4) Hamming code. The proposed system uses a discrete fractional-order system with high computation complexity and only requires pre-iteration once. The combination of state variables produced by the selection mechanism is sensitive to pixel changes, leading to an excellent differential spreading effect that accelerates block diffusion efficiency. The transmission of state variables is hidden in the cipher image through (7, 4) Hamming coding to enhance the security and real-time communication of the system.
MOBILE NETWORKS & APPLICATIONS
(2023)
Article
Computer Science, Information Systems
Madini O. Alassafi, Muhammad Sohail Ibrahim, Imran Naseem, Rayed AlGhamdi, Reem Alotaibi, Faris A. Kateb, Hadi Mohsen Oqaibi, Abdulrahman A. Alshdadi, Syed Adnan Yusuf
Summary: Face presentation attack detection (PAD) is a crucial step in modern face recognition systems to expose imposters and unauthorized persons. This research proposes a novel face PAD solution using interpolation-based image diffusion and transfer learning of a MobileNet convolutional neural network. The experimental results show that the proposed method outperforms most state-of-the-art methods in terms of performance.
Article
Computer Science, Information Systems
Ayesha, Muhammad Javed Iqbal, Iftikhar Ahmad, Madini O. Alassafi, Ahmed S. Alfakeeh, Ahmed Alhomoud
Summary: This research focuses on comprehensive methodology of tiny vehicle detection using Deep Neural Networks (DNN) and achieves better performance compared to other SOTA techniques on KITTI benchmark dataset.
CMC-COMPUTERS MATERIALS & CONTINUA
(2023)
Article
Computer Science, Information Systems
Sabbir Ahmed, Mohammad Abu Yousuf, Muhammad Mostafa Monowar, Abdul Hamid, Madini O. Alassafi
Summary: Depression and anxiety are common mental illnesses that are often overlooked. The current research primarily focuses on one or two factors for detection purposes, failing to consider all possible factors. To address this, researchers have developed a multimodal diagnosis system and proposed an attention-based multimodal classifier that can effectively train different modal datasets. Experimental results have shown that this approach achieves high accuracy, although missing modalities in the model may result in uncertainty in predictions.
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)
