Article
Mathematics, Interdisciplinary Applications
Meng Xu, Pengjian Shang, Sheng Zhang
Summary: In this study, a modification of cumulative residual entropy (CRE) called multiscale Renyi cumulative residual distribution entropy (MRCE) is proposed for investigating the complexity of time series. Results show that MRCE has high sensitivity to predetermined parameters and can analyze the complexity of different time series at different scales. Additionally, financial time series in the same region exhibit obvious similarities.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Silvio Fernando Alves Xavier Junior, Erika Fialho Morais Xavier, Jader Silva Jale, Tatijana Stosic, Carlos Antonio Costa dos Santos
Summary: This study explored the complexity of monthly rainfall temporal series recorded from 1962 to 2012 at 69 meteorological stations in Paraiba state, northeastern Brazil, using the Modified Multiscale Entropy Method. By comparing results across different regions, the study distinguished rainfall patterns and contributed to the use of multiscale approaches in climatological studies.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Computer Science, Information Systems
Xue Wang, Xiaofeng Liu, Wei Pang, Aimin Jiang
Summary: In this research, a novel multiscale analysis method called multiscale increment entropy (MIE) is proposed, which integrates incremental entropy (IncrEn) and multiscale analysis. MIE outperforms popular approaches as a complexity index and corroborates the complexity-loss theory of ageing and disease. It reliably discriminates different types of physiological signals and has shorter computational time, making it suitable for analyzing unknown physiological time series.
INFORMATION SCIENCES
(2022)
Article
Physics, Multidisciplinary
Pierre Bouny, Laurent M. Arsac, Emma Toure Cuq, Veronique Deschodt-Arsac
Summary: Recent research has revealed the existence of a networked system involving cortical and subcortical circuitry regulating cognition and cardiac autonomic control, which is dynamically organized based on cognitive demand. Entropy and (multi)fractality in heart period time series are suitable for capturing emergent behavior of the cognitive-autonomic network coordination.
Article
Mathematics, Interdisciplinary Applications
Yu Wang, Pengjian Shang
Summary: An improved new model, mvMDE, and its fractional order form, GmvMDE, are proposed based on multivariate multiscale dispersion entropy theories. These models effectively measure and distinguish sequence complexity, with GmvMDE better capturing small sequence evolutions. Additionally, MSDE and GMSDE models are introduced to accurately capture systemic complexity of financial portfolios.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2021)
Article
Engineering, Mechanical
Meng Xu, Pengjian Shang, Sheng Zhang
Summary: The study aims to measure the complexity of different types of signals, proposing various methods to explain the intrinsic properties of dynamic systems. Experimental results show that the methods can provide a better understanding of signal complexity when applied to heart rate fluctuation data, distinguishing between healthy and pathological states.
NONLINEAR DYNAMICS
(2021)
Article
Engineering, Mechanical
Yuxing Li, Shangbin Jiao, Yin Zhu, Yujun Li
Summary: In this study, a new complexity-entropy causal plane called the complete ensemble EMD with adaptive noise analysis (CEEMDAN) energy entropy plane is proposed to overcome the mode mixing caused by empirical mode decomposition (EMD), which affects the accuracy of experimental results and analyze the complexity of time series effectively.
NONLINEAR DYNAMICS
(2023)
Article
Physics, Multidisciplinary
Li Wan, Guang Ling, Zhi-Hong Guan, Qingju Fan, Yu-Han Tong
Summary: This paper proposes a new complexity measurement algorithm called multiscale weighted phase permutation entropy (MWPPE) to improve permutation entropy (PE) by utilizing phase transformation, weight influence, and multiscale information for a better understanding of the complexity of nonlinear time series. The method is further extended to fractional order to obtain fractional multiscale phase permutation entropy (FMPPE). The effectiveness of the proposed algorithms is discussed based on simulation sequences, and the results show that they can effectively amplify the detection effect of dynamic changes. Additionally, the FMPPE strategy is found to be more effective than the MWPPE method in distinguishing developed country stock indices from emerging country stock indices.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2022)
Article
Mathematics
Xuyan Xiang, Jieming Zhou
Summary: Long-term memory behavior is an important phenomenon in time series analysis. The excess entropy approach is used to classify long-term and short-term memory in stationary time series. Simulation results demonstrate the effectiveness of the approach on various stochastic sequences. The approach has advantages over traditional methods as it is invariant under instantaneous one-to-one transformation and has weak moment conditions.
Article
Multidisciplinary Sciences
Matthew W. Flood, Bernd Grimm
Summary: Entropy has been increasingly used in various research fields to quantify the regularity, variability, and randomness of time series and image data, yet there is a lack of validated, open-source software tools. EntropyHub is an open-source toolkit that provides a wide range of functions for estimating various entropy methods, aiming to make advanced entropic time series analysis straightforward and reproducible.
Article
Mathematics, Interdisciplinary Applications
Antonio Samuel Alves Silva, Romulo Simoes Cezar Menezes, Osvaldo A. Rosso, Borko Stosic, Tatijana Stosic
Summary: This study analyzed the predictability and complexity of monthly rainfall temporal series in Pernambuco state, northeastern Brazil using complexity entropy causality plane and Fisher Shannon plane. By comparing the positions in these planes, different rainfall regimes in inland, intermediate, and coastal regions were distinguished. Time dependent analysis identified periods of higher entropy related to El Nino episodes and historical droughts in the Sertao region.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Guyue Qin, Pengjian Shang
Summary: This paper introduces a new entropy plane method to quantify the complexity of time series using PTEWP and PREWP, and demonstrates its effectiveness in distinguishing financial markets through simulated and actual data.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Engineering, Civil
Xin Zuo, Chi Zhang, Fengyu Cong, Jian Zhao, Timo Hamalainen
Summary: This study proposes a framework based on multi-scale entropy and bidirectional long short-term memory network to explore driver distraction. The results show that multi-scale entropy notably decreases after distraction and driving performance significantly deviates from the normal state. The framework is useful for mining brain activity information and driver distraction detection in realistic driving scenarios.
IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS
(2022)
Article
Mathematics, Interdisciplinary Applications
Huizi Cui, Lingge Zhou, Yan Li, Bingyi Kang
Summary: This paper introduces a method based on belief entropy to measure the complexity of physiological signals in biological systems. The method has better accuracy and applicability compared to existing entropy algorithms.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
Zhuo Wang, Pengjian Shang
Summary: Researchers have proposed three generalized entropy plane methods for evaluating the complexity of two-dimensional data, analyzed their performance, and applied them to the study of multivariate stock time series. The complexity-entropy causality plane method showed good performance, and multiscale multivariate dispersion entropy method was also proposed.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Hao Liu, Yuzhe Li
Summary: This paper investigates the finite-time stealthy covert attack on reference tracking systems with unknown-but-bounded noises. It proposes a novel finite-time covert attack method that can steer the system state into a target set within a finite time interval while being undetectable.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Nikolay A. Kudryashov, Aleksandr A. Kutukov, Sofia F. Lavrova
Summary: The Chavy-Waddy-Kolokolnikov model with dispersion is analyzed, and new properties of the model are studied. It is shown that dispersion can be used as a control mechanism for bacterial colonies.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Qiang Ma, Jianxin Lv, Lin Bi
Summary: This paper introduces a linear stability equation based on the Boltzmann equation and establishes the relationship between small perturbations and macroscopic variables. The numerical solutions of the linear stability equations based on the Boltzmann equation and the Navier-Stokes equations are the same under the continuum assumption, providing a theoretical foundation for stability research.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Samuel W. Akingbade, Marian Gidea, Matteo Manzi, Vahid Nateghi
Summary: This paper presents a heuristic argument for the capacity of Topological Data Analysis (TDA) to detect critical transitions in financial time series. The argument is based on the Log-Periodic Power Law Singularity (LPPLS) model, which characterizes financial bubbles as super-exponential growth (or decay) with increasing oscillations approaching a tipping point. The study shows that whenever the LPPLS model fits the data, TDA generates early warning signals. As an application, the approach is illustrated using positive and negative bubbles in the Bitcoin historical price.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Xavier Antoine, Jeremie Gaidamour, Emmanuel Lorin
Summary: This paper is interested in computing the ground state of nonlinear Schrodinger/Gross-Pitaevskii equations using gradient flow type methods. The authors derived and analyzed Fractional Normalized Gradient Flow methods, which involve fractional derivatives and generalize the well-known Normalized Gradient Flow method proposed by Bao and Du in 2004. Several experiments are proposed to illustrate the convergence properties of the developed algorithms.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Lianwen Wang, Xingyu Wang, Zhijun Liu, Yating Wang
Summary: This contribution presents a delayed diffusive SEIVS epidemic model that can predict and quantify the transmission dynamics of slowly progressive diseases. The model is applied to fit pulmonary tuberculosis case data in China and provides predictions of its spread trend and effectiveness of interventions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Shuangxi Huang, Feng-Fei Jin
Summary: This paper investigates the error feedback regulator problem for a 1-D wave equation with velocity recirculation. By introducing an invertible transformation and an adaptive error-based observer, an observer-based error feedback controller is constructed to regulate the tracking error to zero asymptotically and ensure bounded internal signals.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Weimin Liu, Shiqi Gao, Feng Xu, Yandong Zhao, Yuanqing Xia, Jinkun Liu
Summary: This paper studies the modeling and consensus control of flexible wings with bending and torsion deformation, considering the vibration suppression as well. Unlike most existing multi-agent control theories, the agent system in this study is a distributed parameter system. By considering the mutual coupling between the wing's deformation and rotation angle, the dynamics model of each agent is expressed using sets of partial differential equations (PDEs) and ordinary differential equations (ODEs). Boundary control algorithms are designed to achieve control objectives, and it is proven that the closed-loop system is asymptotically stable. Numerical simulation is conducted to demonstrate the effectiveness of the proposed control scheme.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Gourav Mandal, Lakshmi Narayan Guin, Santabrata Chakravarty
Summary: The ecological framework investigates the dynamical complexity of a system influenced by prey refuge and alternative food sources for predators. This study provides a thorough investigation of the stability-instability phenomena, system parameters sensitivity, and the occurrence of bifurcations. The bubbling phenomenon, which indicates a change in the amplitudes of successive cycles, is observed in the current two-dimensional continuous system. The controlling system parameter for the bubbling phenomena is found to be the most sensitive. The prediction and identification of bifurcations in the dynamical system are crucial for theoretical and field researchers.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Damian Trofimowicz, Tomasz P. Stefanski, Jacek Gulgowski, Tomasz Talaska
Summary: This paper presents the application of control engineering methods in modeling and simulating signal propagation in time-fractional electrodynamics. By simulating signal propagation in electromagnetic media using Maxwell's equations with fractional-order constitutive relations in the time domain, the equations in time-fractional electrodynamics can be considered as a continuous-time system of state-space equations in control engineering. Analytical solutions are derived for electromagnetic-wave propagation in the time-fractional media based on state-transition matrices, and discrete time zero-order-hold equivalent models are developed and their analytical solutions are derived. The proposed models yield the same results as other reference methods, but are more flexible in terms of the number of simulation scenarios that can be tackled due to the application of the finite-difference scheme.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Yuhao Zhao, Fanhao Guo, Deshui Xu
Summary: This study develops a vibration analysis model of a nonlinear coupling-layered soft-core beam system and finds that nonlinear coupling layers are responsible for the nonlinear phenomena in the system. By using reasonable parameters for the nonlinear coupling layers, vibrations in the resonance regions can be reduced and effective control of the vibration energy of the soft-core beam system can be achieved.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
S. Kumar, H. Roy, A. Mitra, K. Ganguly
Summary: This study investigates the nonlinear dynamic behavior of bidirectional functionally graded plates (BFG) and unidirectional functionally graded plates (UFG). Two different methods, namely the whole domain method and the finite element method, are used to formulate the dynamic problem. The results show that all three plates exhibit hardening type nonlinearity, with the effect of material gradation parameters being more pronounced in simply supported plates.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Isaac A. Garcia, Susanna Maza
Summary: This paper analyzes the role of non-autonomous inverse Jacobi multipliers in the problem of nonexistence, existence, localization, and hyperbolic nature of periodic orbits of planar vector fields. It extends and generalizes previous results that focused only on the autonomous or periodic case, providing novel applications of inverse Jacobi multipliers.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Yongjian Liu, Yasi Lu, Calogero Vetro
Summary: This paper introduces a new double phase elliptic inclusion problem (DPEI) involving a nonlinear and nonhomogeneous partial differential operator. It establishes the existence and extremality results to the elliptic inclusion problem and provides definitions for weak solutions, subsolutions, and supersolutions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Shangshuai Li, Da-jun Zhang
Summary: In this paper, the Cauchy matrix structure of the spin-1 Gross-Pitaevskii equations is investigated. A 2 x 2 matrix nonlinear Schrodinger equation is derived using the Cauchy matrix approach, serving as an unreduced model for the spin-1 BEC system with explicit solutions. Suitable constraints are provided to obtain reductions for the classical and nonlocal spin-1 GP equations and their solutions, including one-soliton solution, two-soliton solution, and double-pole solution.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)