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
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, Applied
Kei Inoue, Tomoyuki Mao, Hidetoshi Okutomi, Ken Umeno
Summary: The Lyapunov exponent is used to quantify the chaos of a dynamical system, while entropic chaos degree is introduced in information dynamics to measure the strength of chaos. Both can be used to compute the chaos degree of a dynamical system. This paper attempts to extend the concept of entropic chaos degree in Euclidean space to enhance the measurement capability of chaos strength in dynamical systems, showing several relations with the Lyapunov exponent.
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS
(2021)
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
Materials Science, Multidisciplinary
Anna Keselman, Laimei Nie, Erez Berg
Summary: This study presents a general criterion for the well-defined regime of exponential growth of the OTOC in spatially extended systems with local interactions. In a random unitary circuit model, a prolonged window of exponential growth can be observed in the presence of weak interactions. The results are based on numerical simulations and analytical treatment of both Clifford and universal random circuits.
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
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
Environmental Sciences
Xuekun Chen, Hongjuan Yang, Zhe Lyu, Changjun Yu
Summary: The study investigates the gravity wave produced by typhoons using high-frequency surface wave radar data. The analysis reveals that the gravity wave spectrum exhibits chaotic properties, indicating short-term predictability but long-term unpredictability.
Article
Mathematics, Interdisciplinary Applications
M. D. Vijayakumar, Alireza Bahramian, Hayder Natiq, Karthikeyan Rajagopal, Iqtadar Hussain
Summary: The paper introduces a quadratic hyperjerk system that can generate chaotic attractors and investigates its dynamical behaviors through Lyapunov exponents and bifurcation diagrams. The study reveals multistability of the system, exploring bistability caused by hidden attractors, as well as the complexity of the system's attractors using sample entropy. Additionally, impulsive control is used to stabilize one of the hyperjerk system equilibrium points, making all real initial conditions become equilibrium points of the basin of attraction.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2021)
Article
Mathematics, Interdisciplinary Applications
Munehisa Sekikawa, Naohiko Inaba
Summary: The paper investigates bifurcation diagrams related to torus doubling and claims that chaotic attractors observed have two Lyapunov exponents exactly zero. However, the researchers found through calculations that one of the Lyapunov exponents is actually slightly positive. Taking the coupling parameter into consideration, they confirmed that the second Lyapunov exponent of the discrete system does not approach zero after torus doubling accumulation with larger values set for the coupling parameter.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2021)
Article
Chemistry, Analytical
Jerzy Margielewicz, Damian Gaska, Grzegorz Litak, Piotr Wolszczak, Shengxi Zhou
Summary: The research in this paper focuses on a new design solution for an energy harvesting system that combines a quasi-zero-stiffness energy harvester and a two-stage flexible cantilever beam. The study includes analysis of the system dynamics and energy generation efficiency. The results suggest that attaching piezoelectric energy transducers to each step of the beam can effectively harvest energy.
Article
Mathematics, Interdisciplinary Applications
Hang Li, Yongjun Shen, Yanjun Han, Jinlu Dong, Jian Li
Summary: This paper proposes a method for determining the Lyapunov exponent spectrum of fractional-order systems, which is derived based on the memory principle of Grunwald-Letnikov derivative. The method is generally applicable and even well compatible with integer-order systems. Simulation results using three classical examples demonstrate the superiority of the proposed method in accuracy and correctness compared to existing methods.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Yanyan Han, Jianpeng Ding, Lin Du, Youming Lei
Summary: This work introduces a method for chaos control and anti-control based on the moving largest Lyapunov exponent using reinforcement learning. A reward function is designed for reinforcement learning according to the moving largest Lyapunov exponent, and a clustering algorithm is adopted to determine a linear region of the average divergence index to obtain the largest Lyapunov exponent. The proposed method is shown to be fast and easy to implement by controlling and anti-controlling typical systems such as the Henon map and Lorenz system.
PHYSICA D-NONLINEAR PHENOMENA
(2021)
Article
Chemistry, Multidisciplinary
Jaehyeon Nam, Jaeyoung Kang
Summary: This study classified chaotic time series data using a convolutional neural network (CNN) and verified it through the Lyapunov exponent. The Lyapunov exponent was calculated by parametric analysis and visualized with a recurrence matrix to show the dynamic characteristics, while the proposed CNN model determined chaos with an accuracy of more than 92%.
APPLIED SCIENCES-BASEL
(2021)
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
Mathematics, Applied
Kei Inoue, Tomoyuki Mao, Hidetoshi Okutomi, Ken Umeno
Summary: The Lyapunov exponent is used to quantify the chaos of a dynamical system, while entropic chaos degree is introduced in information dynamics to measure the strength of chaos. Both can be used to compute the chaos degree of a dynamical system. This paper attempts to extend the concept of entropic chaos degree in Euclidean space to enhance the measurement capability of chaos strength in dynamical systems, showing several relations with the Lyapunov exponent.
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS
(2021)
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.
