Article
Mathematics, Applied
D. Mansouri, S. Bendoukha, S. Abdelmalek, A. Youkana
Summary: This paper investigates the stability and chaos of a time-fractional reaction-diffusion system with the same nonlinearity as the Newton-Leipnik chaotic system. It introduces a nonlinear synchronization controller and proves its convergence using fractional stability theory and the Lyapunov method.
APPLICABLE ANALYSIS
(2021)
Article
Mathematics, Applied
Najat Almutairi, Sayed Saber
Summary: In this paper, a generalized numerical scheme is proposed to simulate variable-order fractional differential operators, and the method is validated through specific examples. The results show that the simulated and analytical results agree, indicating the practical value of this method.
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
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, Interdisciplinary Applications
Abdullah Gokyildirim
Summary: Interest in fractional calculus and its applications has been increasing, and fractional-order analysis has the potential to enhance chaotic systems. This study presents the implementation of a lower-order fractional electronic circuit for the Sprott K system, which is pioneering in achieving a fractional-order parameter of approximately 0.8. Various numerical analyses are conducted to examine the dynamic characteristics and complexity of the system, and the voltage outputs from the oscilloscope show good agreement with the numerical analysis and simulations.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Pongsakorn Sunthrayuth, Hina M. Dutt, Fazal Ghani, Mohammad Asif Arefin
Summary: This article presents a method for solving fractional delay differential equations and combines it with the steps method. The results show that the proposed method is accurate, reliable, and has a fast error convergence rate.
Article
Computer Science, Interdisciplinary Applications
Kulpash Iskakova, Mohammad Mahtab Alam, Shabir Ahmad, Sayed Saifullah, Ali Akguel, Guelnur Yilmaz
Summary: In this article, a new nonlinear four-dimensional hyperchaotic model is presented and analyzed extensively. The research covers various aspects of the complex system, including equilibrium points, stability, dissipation, bifurcations, Lyapunov exponent, phase portraits, Poincare mapping, attractor projection, sensitivity, and time series analysis. The study also explores hidden attractors and investigates the system in the fractional sense. Theoretical and numerical studies reveal the complex dynamics and stimulating physical characteristics of the model.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Engineering, Electrical & Electronic
Pengfei Huang, Fei Qi, Yi Chai, Liping Chen
Summary: This article focuses on the problem of intermittent sensor faults under unknown disturbance and strong noise, and proposes a detection scheme that can effectively mitigate these faults. The proposed scheme is validated through simulation experiments, comparison experiments, and real-world experiments.
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT
(2022)
Article
Mathematics, Interdisciplinary Applications
Vincent-Ademola Adeyemi, Esteban Tlelo-Cuautle, Francisco-Javier Perez-Pinal, Jose-Cruz Nunez-Perez
Summary: The main goal of this research is to optimize the behavior of a three-dimensional chaotic system and compare it with a novel hyperchaotic system. The results show that the optimized system exhibits more complexity, ergodicity, internal randomness, and unpredictability compared to its hyperchaotic counterpart.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Interdisciplinary Applications
Changjin Xu, Mati Ur Rahman, Bibi Fatima, Yeliz Karaca
Summary: This paper presents a theoretical and complex numerical analysis of the 2-torus chaotic system with a power-law kernel. Various dynamical characteristics of the complex system are investigated, including the existence of unique attractors, attractor projection, time series analysis, and sensitivity to initial values. It is observed that coexistence of 4-torus attractors can occur at different fractional orders. The numerical illustrations show that transitioning from higher to lower fractional orders significantly affects the dynamics of the system and shrinks the oscillatory range's geometry. Additionally, new oscillations emerge at lower fractional orders, with lower amplitudes compared to those at higher fractional orders.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Review
Mathematics, Interdisciplinary Applications
Nadjette Debbouche, A. Othman Almatroud, Adel Ouannas, Iqbal M. Batiha
Summary: Modeling the glucose-insulin regulatory system is crucial for treating diabetes, a serious health issue. This study investigates the impact of incommensurate fractional-order derivatives on the model, revealing interesting dynamics such as chaos and coexisting attractors in response to even slight changes in these values. Comparisons with previous models demonstrate a wider presence of chaotic regions when the values of these incommensurate-orders are altered.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Zuanbo Zhou, Wenxin Yu
Summary: This study investigates the phenomenon of stochastic resonance (SR) in higher-dimensional fractional-order systems. By examining the fractional-order Lorenz-like system, the authors present the dynamic process and key parameters of the SR phenomenon. The numerical simulations demonstrate that adjusting the order of the fractional-order system and internal parameters can alter the boundaries and effects of SR.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Engineering, Mechanical
F. M. Kamal, A. Elsaid, A. Elsonbaty
Summary: This paper verifies the occurrence of ghost attractor in a proposed fractional order Rossler blinking system, and explores the dynamical behaviors of the system. It is found that the system is sensitive to system parameters, initial conditions, and stochastic process parameters. The induced chaotic ghost attractor is then utilized in a suggested image encryption scheme, which is immune against different types of attacks.
NONLINEAR DYNAMICS
(2022)
Article
Physics, Multidisciplinary
Zhangzhi Wei, Xin Zhang
Summary: The investigation of dynamical behaviors for fractional-order chaotic systems is a new trend. Numerical analysis of the Shimizu-Morioka model with a fractional order reveals chaos in models with order less than three using fractional calculus techniques. Phase diagrams were also constructed in this study.
FRONTIERS IN PHYSICS
(2021)
Article
Mathematics, Applied
Mohanasubha Ramasamy, Suresh Kumarasamy, Ashokkumar Srinivasan, Pavithra Subburam, Karthikeyan Rajagopal
Summary: This study investigates the influence of higher-order interactions on network synchronization in fractional-order complex systems. The results show that higher-order interactions contribute to earlier synchronization, and lower fractional-order values accelerate the synchronization process. The findings are validated using multiple models.
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)
