Recursive Sparse Identification of Nonlinear Dynamics for Online Equation Discovery by Swadexi Istiqphara, Oyas Wahyunggoro, Adha Imam Cahyadi

“…This method aims to generate mathematical equations for both linear and nonlinear dynamic systems in online streaming data. The proposed method is tested on two nonlinear systems: Lorenz Chaotic System with parameter changes and dataset of KUKA robotic manipulator. …”
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Output Recurrent Fuzzy Broad Learning Systems for Adaptive MIMO PID Control: Theory, Simulations, and Application by Ali Rospawan, Ching-Chih Tsai, Chi-Chih Hung

“…The setpoints tracking control performance and disturbance rejection abilities are firmly illustrated by performing three simulations to the multivariable nonlinear dynamic systems. Moreover, one experimental study to the laboratory-built extrusion barrel in a plastic injection molding machine is done to validate the effectiveness and practicality of the proposed control method. …”
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Study of fractional order dynamics of nonlinear mathematical model by Kamal Shah, Amjad Ali, Salman Zeb, Aziz Khan, Manar A. Alqudah, Thabet Abdeljawad

“…This manuscript is devoted to establishing some theoretical and numerical results for a nonlinear dynamical system under Caputo fractional order derivative. …”
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Nonlinear Normal Modes in a Two-Stage Isolator Using a Modified Finite-Element Galerkin Method by Cheng Li, Hongguang Li

“…Besides the displacement of payload and the force transmissibility of this typical nonlinear dynamic system, the nonlinear normal modes defined as invariant manifolds can provide more information about the nonlinear coupling between the system components when periodic motions corresponding to the normal modes of the system occur. …”
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Investigation of Pedodiversity Indices, Soil Differentiation and Soil-Landscape Evolution in the Semi-Arid Region of Chaharmahal-Va-Bakhtiyari Province by M. Zeraatpisheh, Sh. Ayoubi, H. Khademi, A. Jafari

“…The positive and nonlinear relationship between pedodiversity indices confirmed the nonlinear dynamic system in the studied soils.…”
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A self-adjusting multi-objective control approach for quadrotors by Sallam A. Kouritem, Mohannad Mahmoud, Nabil Nahas, Mohammed I. Abouheaf, Ahmed M. Saleh

“…The quadrotor represents a class of highly nonlinear dynamic systems and its controllability features are challenging. …”
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A new approach to nonlinear modelling of dynamic systems based on fuzzy rules by Bartczuk Łukasz, Przybył Andrzej, Cpałka Krzysztof

“…In this paper we propose a new approach to the modelling of weakly nonlinear dynamic systems. In this approach we assume that the model of the weakly nonlinear system is composed of two parts: a linear term and a separate nonlinear correction term. …”
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Nonlinear dynamic process monitoring using deep dynamic principal component analysis by Simin Li, Shuanghua Yang, Yi Cao, Zuzhen Ji

“…However, it assumes that the value of the variable at each moment is unrelated, which is not suitable for complex nonlinear dynamic system. To address the concerns, by adopting dynamic PCA to extract dynamic features, a new deep approach, namely Deep Dynamic Principal Component Analysis (DeDPCA), is proposed. …”
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Collective vibrations of a hydrodynamic active lattice by Thomson, SJ, Durey, M, Rosales, RR

“…Numerical simulations support our findings and prompt further investigations of this nonlinear dynamical system.…”
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Data-driven discovery of the governing equations of dynamical systems via moving horizon optimization by Fernando Lejarza, Michael Baldea

“…The proposed framework reduces gradient approximation errors by implicitly embedding an advanced numerical discretization scheme, which improves robustness to noise as well as to model stiffness. Canonical nonlinear dynamical system examples are used to demonstrate that our approach can accurately recover parsimonious governing laws under increasing levels of measurement noise, and outperform state of the art frameworks in the literature. …”
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Improving The Manoeuvrability of Electric Vehicle with Four-Wheel Drive and Four-Wheel Steering – A Nonlinear Model Vehicle Dynamics Approach by Ishak M.I., Heerwan P.M., Rasid M.A.H.

“…The dynamics motion of a vehicle is inherently a nonlinear dynamics system especially at high speed. Majority of past researches on four-wheel steering (4WS) vehicle adopt easier way of modelling a control system based on vehicle with linear dynamic equation of motion. …”
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Embedding theory of reservoir computing and reducing reservoir network using time delays by Xing-Yue Duan, Xiong Ying, Si-Yang Leng, Jürgen Kurths, Wei Lin, Huan-Fei Ma

“…Here, combining the delayed embedding theory with the generalized embedding theory, we rigorously prove that RC is essentially a high-dimensional embedding of the original input nonlinear dynamical system. Thus, using this embedding property, we unify into a universal framework the standard RC and the time-delayed RC where we introduce time delays only into the network's output layer, and we further find a trade-off relation between the time delays and the number of neurons in RC. …”
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Theoretical aspects and methods of the parameters identification of the electric traction system devices. the instantaneous powers method; series connection of elements by T.M. Mishchenko

“…Purpose: For this purpose the mathematical model of the nonlinear dynamical system "traction substation – electric traction network – electric rolling stock» as a passive two-terminal network with the given input voltage and input current is proposed. …”
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STRIP ROLLING MILL’S RIGID-FLEXIBLE COUPLING VIBRATION MODELING by ZHANG Yang, PENG Yan, SUN JianLiang, ZANG Yong

“…Tandem strip mill is a complex system composed of a plurality of working frames and auxiliary equipments,each frame is a multi-variable,nonlinear dynamic system,and interacts with the adjacent one by the moving steel strip. …”
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A canonical circuit for generating phase-amplitude coupling. by Angela C E Onslow, Matthew W Jones, Rafal Bogacz

“…Analytic treatment of this circuit as a nonlinear dynamical system demonstrates how connection strengths and inputs to the populations can be varied in order to change the extent and nature of PAC activity, importantly which phase of the lower frequency rhythm the higher frequency activity is locked to. …”
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Convergence map with action-angle variables based on square matrix for nonlinear lattice optimization by Li Hua Yu, Yoshiteru Hidaka, Victor Smaluk, Kelly Anderson, Yue Hao

“…To analyze nonlinear dynamic systems, we developed a new technique based on the square matrix method. …”
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High-Order Control Lyapunov–Barrier Functions for Real-Time Optimal Control of Constrained Non-Affine Systems by Alaa Eddine Chriat, Chuangchuang Sun

“…This paper presents a synthesis of higher-order control Lyapunov functions (HOCLFs) and higher-order control barrier functions (HOCBFs) capable of controlling nonlinear dynamic systems while maintaining safety. Building on previous Lyapunov and barrier formulations, we first investigate the feasibility of the Lyapunov and barrier function approach in controlling a non-affine dynamic system under certain convexity conditions. …”
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Using entropy-driven amplifier circuit response to build nonlinear model under the influence of Lévy jump by Hao Fu, Hui Lv, Qiang Zhang

“…Results In this paper, nonlinear dynamic system model with Lévy jump based on entropy-driven amplifier (EDA) circuit response is studied. …”
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On the many-body problem with short-range interaction by Mark M. Gambaryan, Mikhail D. Malykh

“…Difficulties in the mathematical description of short-range interaction are discussed, for which it is necessary to combine two models, a nonlinear dynamic system describing the motion of particles in a field, and a boundary value problem for a hyperbolic equation or Maxwells equations describing the field. …”
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Stochastic Response of Composite Post Insulators under Seismic Excitation by Haibo Wang, Yongfeng Cheng, Zhicheng Lu, Ronghua Huan, Qiangfeng Lü, Zhenlin Liu

“…First, a stochastic ground motion model, conforming to the Code for Seismic Design of Electrical Insulators in China, is established, incorporating amplitude and frequency non-stationarity. Next, the nonlinear dynamic system, accounting for multi-section composite post insulators and the nonlinearity of flange connections, is established under stochastic ground motion conditions. …”
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