Article
Engineering, Multidisciplinary
Guohui Li, Yongming Hou, Hong Yang
Summary: The proposed differential double coupled Duffing oscillator method provides a more intuitive way to judge large scale states and overcomes frequency limitations, showing high signal-to-noise ratio and universality in detecting various background signals.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Engineering, Mechanical
Mengfei Cheng, Weiwei Zhang, Jing Wu, Hongwei Ma
Summary: In this study, a double chaotic detection system was proposed to identify weak defect echo signals caused by small defects during ultrasonic guided wave nondestructive testing of pipelines. By quantitatively detecting the amplitude and time of flight (ToF) of defect echoes, minor defects in early damage identification of pipelines were detected. The method could simultaneously identify the size and ToF of ultrasonic guided waves, even at low signal-to-noise ratios (SNR). The identification error of the amplitude was only 8%, indicating acceptable detection results. The method effectively improved the sensitivity of ultrasonic guided waves in detecting small defects in pipelines.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2023)
Article
Chemistry, Analytical
Yi Yang, Fei Li, Nan Zhang, Aiqing Huo
Summary: This paper utilizes stochastic resonance and chaos phase transition to identify the frequency and estimate the parameters of the measurement while drilling signal, providing a solution to the deviation of the well path caused by attitude measurement errors. The proposed algorithm shows good immunity to interference noise, improving the accuracy of inclination solution and ensuring the dynamic stability of the well trajectory in a severe noise environment.
Article
Engineering, Mechanical
Kaifeng Dong, Kun Xu, Youyou Zhou, Chao Zuo, Leimin Wang, Chuanke Zhang, Fang Jin, Junlei Song, Wenqin Mo, Yajuan Hui
Summary: A new type of weak signal detection system that combines the memristor and Van der pol-Duffing chaotic system has been proposed in this paper. The system can change from a chaotic state to a periodic state under different driving force amplitudes. The numerical simulation results show that the detection accuracy of the system is high and the anti-noise performance is doubled.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Electrical & Electronic
Dawei Chen, Shuo Shi, Xuemai Gu, Byonghyo Shim
Summary: Chaos theory benefits from its sensitivity and immunity in weak signal detection, showing promising performance in various communication scenarios. Through different chaos-based approaches, satisfactory performance has been achieved, as demonstrated by theoretical analysis and numerical simulations, indicating excellent accuracy and robustness.
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY
(2021)
Article
Physics, Multidisciplinary
Kei Inoue
Summary: The paper discusses the application of Lyapunov exponent and entropic chaos degree in quantifying chaos in dynamical systems, with a focus on reducing the difference between the two measures. It also presents an extension of the improved entropic chaos degree for multi-dimensional chaotic maps and proposes an improved calculation formula for obtaining suitable numerical computation results for two-dimensional chaotic maps.
Article
Physics, Multidisciplinary
Kei Inoue
Summary: The Lyapunov exponent is a commonly used measure for quantifying chaos in a dynamical system, but its computation requires specific information. The entropic chaos degree quantifies chaos in a dynamical system as an information quantity and can be computed directly for any time series, regardless of knowledge about the dynamical system. A recent study introduced the extended entropic chaos degree, which achieved the same value as the sum of Lyapunov exponents under typical chaotic conditions. An improved computation formula for the extended entropic chaos degree was proposed to obtain accurate numerical results for multidimensional chaotic maps. This study demonstrates that all Lyapunov exponents of a chaotic map can be estimated to compute the extended entropic chaos degree and proposes a computational algorithm for it, which was applied to one and two-dimensional chaotic maps. The results suggest that the extended entropic chaos degree may serve as a viable alternative to the Lyapunov exponent for both one and two-dimensional chaotic dynamics.
Article
Mathematics, Interdisciplinary Applications
Zayneb Brari, Safya Belghith
Summary: This paper investigates the complex behavior and noise contamination issues in electroencephalographic signals (EEG) and proposes an algorithm for chaotic signal analysis based on the determination of the Largest Lyapunov Exponent (LLE). The proposed method is validated using various chaotic attractors and achieves a low error rate in LLE estimation even in the presence of noise. Additionally, a supervised machine learning model for epilepsy and seizure detection is proposed and achieves 100% accuracy in different classification cases using only 4 features.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Engineering, Mechanical
Mainul Hossain, Ruma Kumbhakar, Nikhil Pal, Juergen Kurths
Summary: Migration is a natural behavior found in many species, including mammals, birds, fish, and insects. Animals migrate in response to environmental factors such as food availability, habitat safety, climate, and mating opportunities. This study examines how the migration of middle predators affects the dynamics of a tri-trophic food chain model and finds that moderate migration promotes regularity in the system, while high migration rates can lead to species extinction.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Vahid Khodadadi, Fereidoun Nowshiravan Rahatabad, Ali Sheikhani, Nader Jafarnia Dabanloo
Summary: Chaos in the electromyographic (EMG) signal of the biceps muscle is detected and quantified using nonlinear features. Understanding the behavior of these complex and nonlinear systems, which can be chaotic, is important for understanding diseases, finding treatments, and using rehabilitation equipment.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Physics, Mathematical
Kajal Krishna Dey, Golam Ali Sekh
Summary: In the case of fixed stiffness, strong correlated random excitations distort the Poincare map, making it purely random, while random response competes with chaotic motion to enhance system stability. In the case of periodically modulated stiffness, random fields can change the system's state from transient to stable.
JOURNAL OF STATISTICAL PHYSICS
(2021)
Article
Engineering, Chemical
William D. Fullmer, Roberto Porcu, Jordan Musser, Ann S. Almgren, Ishan Srivastava
Summary: The study investigates n-body instability using the soft-sphere discrete element method, quantifying divergence of nearby trajectories with the dynamical memory time. By comparing results with hard-sphere molecular dynamics data, it is found that the soft-sphere method shows good agreement at low concentrations and increasing instability with higher particle concentrations. Furthermore, the soft-sphere Lyapunov exponents increase faster than the corresponding hard-sphere data at concentrations above 30%.
Article
Mathematics, Interdisciplinary Applications
Kei Inoue, Kazuki Tani
Summary: This paper introduces a quantification method for chaos in traffic flow models. The extended entropic chaos degree can directly compute the chaos level of time series with lower computational complexity. Through empirical research, it is demonstrated that the extended chaos degree can be used to quantify chaos in traffic flow models.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Derya Sekman, Vatan Karakaya
Summary: This article explores the relationship between chaos and dynamical systems, focusing on the iteration processes related to fixed point theory. The main emphasis is on controlling chaos in fixed point iteration dynamics, and analytical solutions and parameter adjustment methods are proposed. Through case studies of various iteration processes, especially a detailed investigation of the Noor iteration process, the article presents a method for estimating the stability of chaos. Finally, the results are validated using MATLAB programs on equations exhibiting chaotic properties.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
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)
