Grazing Orbits and Related Local Bifurcations of an Oscillator with Continuous and Piecewise-Linear Restoring Force by Haiyan Hu

“…Then, through a brief analysis, the article shows that the grazing phenomenon turns the stability trend of the periodic orbit so abruptly that it may be impossible to predict an incident local bifurcation with the variation of a control parameter from the concept of smooth dynamic systems. The numerical simulation in the article well supports the scheme and the analysis, and shows an abundance of grazing phenomena in an engineering range of the excitation frequency.…”
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Eigenpairs for the Analysis of Complete Lyapunov Functions by Carlos Argáez, Peter Giesl, Sigurdur Freyr Hafstein

“…A complete Lyapunov function describes the qualitative behaviour of a dynamical system: the areas where the orbital derivative vanishes and where it is strictly negative characterise the chain recurrent set and the gradient-like flow, respectively. …”
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Position Tracking Control for Permanent Magnet Linear Motor via Continuous-Time Fast Terminal Sliding Mode Control by Wei Gao, Xiuping Chen, Haibo Du, Song Bai

“…Specifically, first, for the second-order model of position error dynamic system, a new continuous-time fast terminal sliding surface is introduced and an improved continuous-time fast terminal sliding mode control law is proposed. …”
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The traveling wave solution and dynamics analysis of the fractional order generalized Pochhammer–Chree equation by Chunyan Liu

“…Second, the dynamic behavior is analyzed using the planar dynamical system, and some three-dimensional and two-dimensional phase portraits are drawn using Maple software to reflect its chaotic behaviors. …”
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On the derivation of the nonlinear discrete equations numerically integrating the Euler PDEs by F. N. Koumboulis, M. G. Skarpetis, B. G. Mertzios

“…The Euler equations, namely a set of nonlinear partial differential equations (PDEs), mathematically describing the dynamics of inviscid fluids are numerically integrated by directly modeling the original continuous-domain physical system by means of a discrete multidimensional passive (MD-passive) dynamic system, using principles of MD nonlinear digital filtering. …”
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Consilience of Reductionism and Complexity Theory in Language Research: Adaptive Weight Model by Chao Zhang

“…This paper starts by discussing the adaptability of complex dynamic systems and combines cognitive processing model and artificial neural networks to construct and verify an adaptive weight model, showing that the study of reductionism is induction of high-weight elements and the study of complexity theory is a discussion of system complexity from adaptability, meaning that there is a good fit between the two frameworks. …”
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Multiparty Evolutionary Game Model in Coal Mine Safety Management and Its Application by Rongwu Lu, Xinhua Wang, Hao Yu, Dan Li

“…Based on stability theory of dynamics system and phase diagram analysis, this article studies replicator dynamics of the evolutionary model to make an optimization analysis of the behaviors of those interested parties and the adjustment mechanism of safety management policies and decisions. …”
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Analysis of Complex Dynamics in Different Bargaining Systems by Xiaogang Ma, Chunyu Bao, Lin Su

“…We explore the influence of bargaining power and adjustment speed on the stability of the dynamic system and find that both of the factors need to be small to maintain the stability of the supply chain. …”
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Distributed Filter with Consensus Strategies for Sensor Networks by Xie Li, Huang Caimou, Hu Haoji

“…Consensus algorithm for networked dynamic systems is an important research problem for data fusion in sensor networks. …”
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Proportional PDC Design-Based Robust Stabilization and Tracking Control Strategies for Uncertain and Disturbed T-S Model by Chekib Ghorbel, Amira Tiga, Naceur Benhadj Braiek

“…This paper presents a proportional parallel distributed compensation (PPDC) design to the robust stabilization and tracking control of the nonlinear dynamic system, which is described by the uncertain and perturbed Takagi–Sugeno (T-S) fuzzy model. …”
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Detailed Theoretical Model for Adjustable Gain-Clamped Semiconductor Optical Amplifier by Lin Liu, Craig Michie, Anthony E. Kelly, Ivan Andonovic

“…This type of subsystem can be used for power equalisation and linear amplification in packet-based dynamic systems such as passive optical networks (PONs). …”
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An evaluation of dynamic outlet boundary conditions in a 1D fluid dynamics model by Rachel Clipp, Brooke Steele

“…This study implements a dynamic impedance outlet boundary condition in a one-dimensional fluid dynamics model using the pulmonary vasculature and respiration (feedback mechanism) as an example of a dynamic system. The dynamic boundary condition was successfully implemented and the pressure and flow were predicted for an entire respiration cycle. …”
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Evolutionary Stability Analysis of the Coal Mine Safety Management System Governed by Delay and Impulsive Differential Equations by Li Bai, Xinhua Wang, Rongwu Lu, Hao Yu, Dan Li

“…To study the regular pattern of behavior propagations in CMSM, a series of evolutionary dynamical system models are established by the delay and impulsive differential equations (DIDEs). …”
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Forecast of Chemical Export Trade Based on PSO-BP Neural Network Model by Na Li, Meng Li

“…The neural network is a nonlinear dynamic system, with strong nonlinear mapping ability, strong robustness, and fault tolerance. …”
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Investigating wave solutions in coupled nonlinear Schrödinger equation: insights into bifurcation, chaos, and sensitivity by Adil Jhangeer, Abdallah M. Talafha, Ariana Abdul Rahimzai, Lubomír Říha

“…The model is converted into a dynamical system, enabling qualitative and sensitivity analysis. …”
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Buckling suppression of a cantilever structure with a modified fuzzy sliding mode control by Jianhua Pan, Lin Sun, Xiaopei Liu, Yuyuan Zhang, Yili Duo

“…Therefore, a new active control strategy for large-amplitude buckling suppression of a two-dimensional nonlinear dynamic system of a cantilever beam is established and implemented, effectively suppressing the large-amplitude buckling response in numerical studies.…”
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Adaptive Output Tracking of Driven Oscillators by Lili Diao, Martin Guay

“…For a class of nonlinear dynamic systems with unknown nonlinearities and nonaffine control input, a Lyapunov-based technique is used to develop a control law. …”
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Finite-Time Stability Analysis: A Tutorial Survey by Honglei Xu

“…After a brief introduction to notations and two distinct finite-time stability concepts, dynamical system models, particularly in the form of linear time-varying systems and impulsive linear systems, are studied. …”
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Research on the Numerical Simulation of the Nonlinear Dynamics of a Supercavitating Vehicle by Tianhong Xiong, Xianyi Li, Yipin Lv, Wenjun Yi

“…In this paper, based on a four-dimensional dynamical system of this vehicle, its complicated dynamical behaviors were analyzed in detail by numerical simulation, according to the phase trajectory diagram, the bifurcation diagram, and the Lyapunov exponential spectrum. …”
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Dynamics of a brake system governed by modified Burridge-Knopoff-Pad model by Oma Nfor Nkeh, Akoni Brikly Njinabo, Waindim Yisa Tufoin Albert, Kenfack Djifack Hunnel

“…Result of numerical simulations clearly underscores the displacement and velocity profiles of the block-pad brake dynamical system.…”
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