Rolling Bearing Dynamics Response and Parameter Sensitivity Analysis based on the Response Surface Method by Shi Jialian, Ma Xiaogang, Li Chang, Xie Kuiqiu

“…The dynamics model of rolling bearing of automotive engine bearing-rotor system is established and the nonlinear dynamics differential equation is derived. The numerical solution is obtained by MATLAB after nondimensionalization,the change rule of dynamic response of rolling bearing is obtained. …”
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Hopf Bifurcation in a Cobweb Model with Discrete Time Delays by Luca Gori, Luca Guerrini, Mauro Sodini

“…The dynamics of the economy is characterised by a one-dimensional delay differential equation. In this context, we show that (1) if the elasticity of market demand is sufficiently high, the steady-state equilibrium is locally asymptotically stable and (2) if the elasticity of market demand is sufficiently low, quasiperiodic oscillations emerge when the time lag (that represents the length of production cycle) is high enough.…”
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Longitudinal Vibration and Stability Analysis of Conveying Belt of Belt Conveyor by Man Zhang, Haoxuan Jin, Yongqiang Yang, Yuanhu Cheng, Taisong Guo

“…The differential equation of longitudinal vibration of the belt conveyor with stable conveying speed is established based on Kelvin-Voigt viscoelastic theory. …”
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Taking into account the lens geometric distortion during accumulation of blurred star images in an astro-inertial attitude sensor by S. N. Vasilyuk

“…The analytical approach uses a model of direct distortion correction, which makes it possible to obtain a new differential equation for the blur trajectory in the image plane with distortion. …”
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Uniformly Convergent Nonpolynomial Spline Method for Singularly Perturbed Robin-Type Boundary Value Problems with Discontinuous Source Term by Habtamu Garoma Debela, Gemechis File Duressa

“…In this paper, a singularly perturbed second-order ordinary differential equation with discontinuous source term subject to mixed-type boundary conditions is considered. …”
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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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Determination of the response of a class of nonlinear time invariant systems by Sudhangshu B. Karmakar

“…The system under investigation is assumed to be described by a nonlinear differential equation with forcing term. The response of the system is first obtained in terms of the input in the form of a Volterra functional expansion. …”
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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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Numerical Treatment on Parabolic Singularly Perturbed Differential Difference Equation via Fitted Operator Scheme by Dagnachew Mengstie Tefera, Awoke Andargie Tiruneh, Getachew Adamu Derese

“…This paper proposes a new fitted operator strategy for solving singularly perturbed parabolic partial differential equation with delay on the spatial variable. …”
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On the Korteweg-de Vries equation: an associated equation by Eugene P. Schlereth, Ervin Y. Rodin

“…The purpose of this paper is to describe a relationship between the Korteweg-de Vries (KdV) equation ut−6uux+uxxx=0and another nonlinear partial differential equation of the form zt+zxxx−3zxzxxz=H(t)z.The second equation will be called the Associated Equation (AE) and the connection between the two will be explained. …”
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Kinetic Analysis for Macrocyclizations Involving Anionic Template at the Transition State by Vicente Martí-Centelles, M. Isabel Burguete, Santiago V. Luis

“…The corresponding differential equation systems for each kinetic model can be solved numerically. …”
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Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect by Wenjie Hu, Hua Zhao, Tao Dong

“…Moreover, the normal form of Hopf bifurcations is obtained by using the center manifold theorem and normal form theory of the partial differential equation, which can determine the bifurcation direction and the stability of the periodic solutions. …”
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Asymptotic Behavior of Solutions to a Vector Integral Equation with Deviating Arguments by Cristóbal González, Antonio Jiménez-Melado

“…In the case of q(t,s)=(t-s)+, its solutions with asymptotic behavior given by ω(t) yield solutions of the second order nonlinear abstract differential equation y''(t)-ω''(t)+F(t,y(γ1(t)),…,y(γN(t)))=0, with the same asymptotic behavior at ∞ as ω(t).…”
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Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer Coefficient by Te-Wen Tu, Sen-Yung Lee

“…By dividing the Biot function into a constant plus a function and introducing two specially chosen shifting functions, the system is transformed into a partial differential equation with homogenous boundary conditions only. …”
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DYNAMIC CHARACTERISTICS ANALYSIS OF FLEXIBLE FOUNDATION VIBRATION ISOLATION SYSTEM by ZHANG DaoKun, HUO Rui, LI ShuYing, WANG ZhiDong

“…By transforming the system dynamic equation into an expression of initial value problem of differential equation,the calculation method of transmitted power flow is deduced,which is put forward to evaluation and analysis of isolation effectiveness. …”
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Analysis of the Thermo-elastic for Involute Spur Gear Transmission with Logarithmic Modification by Jin Tingting, Wang Jiugen, Wang Zhenrong

“…Aiming at the involute spur gear with logarithmic modification,according to the heat conduction differential equation and the basic equations of thermo-elasticity,the thermal and thermo-elastic fields of involute spur gear at any meshing position are obtained by using the FFT and IFFT programming calculation,the influence of the torque and rotational speed on temperature field and thermal elastic field is discussed.The results show that,the logarithmic modification can reduce the strong thermal at the edges of the gear tooth caused by the edge effect,thus the scuffing resistance,accuracy and thermal fatigue life of gears are improved.The rising of either torque or rotational speed can intensify the temperature field and thermo-elastic field of gear,and the modification amount should be designed in terms of torque in order to avoid the edge effect.…”
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Ring-Shaped Potential and a Class of Relevant Integrals Involved Universal Associated Legendre Polynomials with Complicated Arguments by Wei Li, Chang-Yuan Chen, Shi-Hai Dong

“…We find that the solution of the polar angular differential equation can be written as the universal associated Legendre polynomials. …”
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Obtaining the Soliton Type Solutions of the Conformable Time-Fractional Complex Ginzburg–Landau Equation with Kerr Law Nonlinearity by Using Two Kinds of Kudryashov Methods by Arzu Akbulut

“…Thus, using the suitable wave transform, the given equation is converted into an ordinary differential equation. Then, the proposed methods are applied to the reduced equation. …”
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Neural-Network-Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real Matrices by Xiongfei Zou, Ying Tang, Shirong Bu, Zhengxiang Luo, Shouming Zhong

“…Although the ordinary differential equation on which our proposed algorithm is built is only n-dimensional, it can succeed to extract n-dimensional complex eigenvectors that are indeed 2n-dimensional real vectors. …”
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Analytical Approximate Solutions for the Cubic-Quintic Duffing Oscillator in Terms of Elementary Functions by A. Beléndez, M. L. Alvarez, J. Francés, S. Bleda, T. Beléndez, A. Nájera, E. Arribas

“…To do this, we use the previous results obtained using a cubication method in which the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a cubic Duffing equation. …”
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