Brock's approaching zero method improved as approaching fixed point frequency to solve optimum damping ratio of dynamic vibration absorber in machine tools and experimental confirm... by Hongliang Tian, Xixiao Liang, Xuan Du

“…Some exact closed-form solutions, for example displacement amplitude gain, fixed point coordinate, and optimum damping ratio, were deduced with the real number form of differential equation of load motion and employing L'Hospital first rule. …”
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Analytical Models for Gravitating Radiating Systems by B. P. Brassel, S. D. Maharaj, G. Govender

“…We show that the isotropy of pressure is a consistency condition which realises a second order nonlinear ordinary differential equation with variable coefficients in the gravitational potentials. …”
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Three-Party Stochastic Evolutionary Game Analysis of Reward and Punishment Mechanism for Green Credit by Qingfeng Zhu, Kaimin Zheng, Yilin Wei

“…We gave sufficient conditions for the stability of strategy based on the stability discriminant theorem of Ito^'s stochastic differential equation (SDE). Then, we discussed the impacts of incentive and penalty parameters on green credit. …”
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A note on the global properties of an age-structured viral dynamic model with multiple target cell populations by Shaoli Wang, Jianhong Wu, Libin Rong

“…We also show that under some scenarios the age-structured model can be reduced to an ordinary differential equation system with or without time delays.…”
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Creeping Ray Tracing Algorithm for Arbitrary NURBS Surfaces Based on Adaptive Variable Step Euler Method by Song Fu, Yun-Hua Zhang, Si-Yuan He, Xi Chen, Guo-Qiang Zhu

“…In differential geometry, geodesic paths satisfy geodesic differential equation (GDE). Hence, in this paper, a general and efficient adaptive variable step Euler method is introduced for solving the GDE on arbitrarilyshaped NURBS surfaces. …”
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Analytical Solutions to Two-Dimensional Nonlinear Telegraph Equations Using the Conformable Triple Laplace Transform Iterative Method by Alemayehu Tamirie Deresse

“…According to the findings, the proposed method is being used to solve additional forms of nonlinear fractional partial differential equation systems. Moreover, the conformable fractional triple Laplace transform iterative method has a small computational size as compared to other methods.…”
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Uniqueness and Asymptotic Behavior of Positive Solutions for a Fractional-Order Integral Boundary Value Problem by Min Jia, Xin Liu, Xuemai Gu

“…The existence, uniqueness, and asymptotic behavior of positive solutions to the singular nonlocal integral boundary value problem for fractional differential equation are obtained. Our analysis relies on Schauder's fixed-point theorem and upper and lower solution method.…”
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Optimal Treatment Strategies for HIV with Antibody Response by Yinggao Zhou, Kuan Yang, Kai Zhou, Chunling Wang

“…An HIV model of ordinary differential equation, which includes immune response, neutralizing antibodies, and multidrug effects, is improved. …”
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The Holling Type II Population Model Subjected to Rapid Random Attacks of Predator by Jevgeņijs Carkovs, Jolanta Goldšteine, Kārlis Šadurskis

“…If the predators’ gains and the time intervals between predator attacks are sufficiently small, our proposed method allows us to derive an approximative average dynamical system for mathematical expectations of population dynamics and the stochastic Ito differential equation for the random deviations from the average motion. …”
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Interval Shannon Wavelet Collocation Method for Fractional Fokker-Planck Equation by Shu-Li Mei, De-Hai Zhu

“…Then, combining with the finite difference technology, a new numerical method for the time fractional partial differential equation is constructed. A simple Fokker-Planck equation is taken as an example to illustrate the effectiveness by comparing with the Grunwald-Letnikov central difference approximation (GL-CDA).…”
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Dynamics Analysis of a Class of Delayed Economic Model by Chuangxia Huang, Changlin Peng, Xiaohong Chen, Fenghua Wen

“…This investigation aims at developing a methodology to establish stability and bifurcation dynamics generated by a class of delayed economic model, whose state variable is described by the scalar delay differential equation of the form d2p(t)/dt2=−μδ(p(t))(dp(t)/dt)−μbp(t−τ1) −μ(a0p(t−τ2)/(a1+p(t−τ2)))+μ(d0−g0). …”
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On the Stability of Eccentrically Compressed Reinforced Concrete Elements with a Small Eccentricity, Taking into Account the Rheological Properties of Concrete by A. G. Tamrazyan

“…Complicated integration is replaced by the solution of the differential equation of the bent axis of the rod in the form of a sinusoid half-wave.…”
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Response of Composite Beam Structure under Unbalanced Excitation of Rice Threshing System by Xujun Zhai, Xingqin You, Hao Zhang, Zhong Tang, Xinzhong Wang, Guoqiang Wang

“…This paper studies the dynamic response of the support beam under the unbalanced excitation of the rice threshing system. The differential equation of motion of the supporting beam under the action of harmonic force is established by the modal superposition method, and its dynamic response is analyzed. …”
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Research on the Trajectory Model for ZY-3 by Yifu Chen, Zhong Xie

“…Meanwhile, the differential equation is derivate for the bundle block adjustment. …”
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Pull-In and Snap-Through Analysis of Electrically Actuated Viscoelastic Curved Microbeam by Ehsan Akrami-Nia, Hamid Ekhteraei-Toussi

“…By applying the Galerkin method, the obtained governing equation is discretized, converted to a nonlinear differential equation, and solved by MATLAB software. Through a quasi-static analysis, the voltage and location of snap-through and pull-in instabilities are identified. …”
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Optimal control of infectious diseases using vaccination and treatment by Maryam Nikbakht

“…For this purpose, an optimal control problem with the objective function is introduced, and vaccination and treatment are considered control variables.Methodology:  In this study, the necessary control conditions and the existence of optimal control are expressed by applying the control to the SIR-differential equation system. The experimental results are compared with those obtained from the fourth-order runge-kutta scheme. …”
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Thermal Diffusivity Identification of Distributed Parameter Systems to Sea Ice by Liqiong Shi, Zhijun Li, Enmin Feng, Yila Bai, Yu Yang

“…A method of optimal control is presented as a numerical tool for solving the sea ice heat transfer problem governed by a parabolic partial differential equation. Taken the deviation between the calculated ice temperature and the measurements as the performance criterion, an optimal control model of distributed parameter systems with specific constraints of thermal properties of sea ice was proposed to determine the thermal diffusivity of sea ice. …”
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The Lagrangian and Hamiltonian for the Two-Dimensional Mathews-Lakshmanan Oscillator by Wang Guangbao, Ding Guangtao

“…The purpose of this paper is to illustrate the theory and methods of analytical mechanics that can be effectively applied to the research of some nonlinear nonconservative systems through the case study of two-dimensionally coupled Mathews-Lakshmanan oscillator (abbreviated as M-L oscillator). (1) According to the inverse problem method of Lagrangian mechanics, the Lagrangian and Hamiltonian function in the form of rectangular coordinates of the two-dimensional M-L oscillator is directly constructed from an integral of the two-dimensional M-L oscillators. (2) The Lagrange and Hamiltonian function in the form of polar coordinate was rewritten by using coordinate transformation. (3) By introducing the vector form variables, the two-dimensional M-L oscillator motion differential equation, the first integral, and the Lagrange function are written. …”
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Dynamical Analysis for the Hybrid Network Model of Delayed Predator-Prey Gompertz Systems with Impulsive Diffusion between Two Patches by Li Xiang, Yurong Zhang, Dan Zhang, Zhichun Yang, Lingzhi Huang

“…Furthermore, by employing the theory of delay functional and impulsive differential equation, we obtain sufficient condition with time delay for the permanence of the network.…”
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Synchronization of the Coupled Distributed Parameter System with Time Delay via Proportional-Spatial Derivative Control by Kun Yuan, Abdulaziz Alofi, Jinde Cao, Abdullah Al-Mazrooei, Ahmed Elaiw

“…By combining parabolic partial differential equation (PDE) theory with Lyapunov technique, the synchronization is studied for a class of coupled distributed parameter systems (DPS) described by PDEs. …”
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