Forecast of Chemical Export Trade Based on PSO-BP Neural Network Model by Na Li, Meng Li

“…The export trade is affected by various domestic and international factors and is a complex nonlinear system. Although the traditional linear prediction method has the advantages of intuitiveness, simplicity, and strong interpretability, it is difficult to deal with the prediction problem of dynamic and complex nonlinear systems. …”
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Adaptive Neural Network-Based Satellite Attitude Control by Using the Dynamic Inversion Technique and a VSCMG Pyramidal Cluster by Mihai Lungu, Romulus Lungu

“…Starting from the dynamic model of the pyramidal cluster, an adaptive control law is designed by means of the dynamic inversion method and a feed-forward neural network-based nonlinear subsystem; the control law has a proportional-integrator component (for the control of the reduced-order linear subsystem) and an adaptive component (for the compensation of the approximation error associated with the function describing the dynamics of the nonlinear system). The software implementation and validation of the new control architecture are achieved by using the Matlab/Simulink environment.…”
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Solutions of Conformable Fractional-Order SIR Epidemic Model by Atimad Harir, Said Malliani, Lalla Saadia Chandli

“…These models are nonlinear system of conformable fractional differential equation (CFDE) that has no analytic solution. …”
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INCREMENTAL HARMONIC BALANCE METHOD FOR THE STUDY OF SUPPORT LOOSENESS FAULT’S CHARACTERISTICS by CAO QingSong, XIANG Qin, XIONG GuoLiang

“…Meanwhile,the validity of solving nonlinear system by incremental harmonic balance method was proved,and the results laid a theoretical foundation for the diagnosis of support looseness fault.…”
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A Toeplitz Jacobian Matrix/Fast Fourier Transformation Method for Steady-State Analysis of Discontinuous Oscillators by T. Ge, A. Y. T. Leung

“…A semianalytical algorithm is proposed for the solutions and their stability of a piecewise nonlinear system. The conventional harmonic balance method is modified by the introduction of Toeplitz Jacobian matrices (TJM) and by the alternative applications of fast Fourier transformation (FFT) and its inverse. …”
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Weak solutions of unconditionally stable second-order difference schemes for nonlinear sine-Gordon systems by Ozgur Yildirim

“…This paper presents the existence and uniqueness of the weak solution for the nonlinear system of sine-Gordon equations which describes DNA dynamics. …”
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Third-Order Approximate Solution of Chemical Reaction-Diffusion Brusselator System Using Optimal Homotopy Asymptotic Method by Salem Alkhalaf

“…It is observed that the method is easy to implement and quite valuable for handling nonlinear system of partial differential equations and yielding excellent results at minimum computational cost. …”
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Stability analysis for first-order nonlinear differential equations with three-point boundary conditions by Kamala E. Ismayilova

“…Several theorems are proved concerning the existence and uniqueness of solutions to the boundary value problems for the first order nonlinear system of ordinary differential equations with three-point boundary conditions. …”
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The formal Laplace-Borel transform of Fliess operators and the composition product by Yaqin Li, W. Steven Gray

“…This gives a compact interpretation of the operational calculus of Fliess for computing the output response of an analytic nonlinear system.…”
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A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation by Liquan Mei, Yali Gao, Zhangxin Chen

“…In addition, an extrapolation technique is used to transform a nonlinear system into a linear system in order to improve the time accuracy of this method. …”
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Series Solution of the Multispecies Lotka-Volterra Equations by Means of the Homotopy Analysis Method by A. Sami Bataineh, M. S. M. Noorani, I. Hashim

“…The continuous solution for the nonlinear system is given, which provides a convenient and straightforward approach to calculate the dynamics of the system. …”
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Alternative Legendre Polynomials Method for Nonlinear Fractional Integro-Differential Equations with Weakly Singular Kernel by Guodong Shi, Yanlei Gong, Mingxu Yi

“…The operational matrices of integration and product together with the derived operational matrix are utilized to transform nonlinear fractional integro-differential equations to the nonlinear system of algebraic equations. Furthermore, the proposed method has also been analyzed for convergence, particularly in context of error analysis. …”
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Neural Network Inverse Model Control Strategy: Discrete-Time Stability Analysis for Relative Order Two Systems by M. A. Hussain, Jarinah Mohd Ali, M. J. H. Khan

“…This paper discusses the discrete-time stability analysis of a neural network inverse model control strategy for a relative order two nonlinear system. The analysis is done by representing the closed loop system in state space format and then analyzing the time derivative of the state trajectory using Lyapunov’s direct method. …”
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Self-organization through decoupling by Romar Correa

“…Formally, a conditionally stable nonlinear system of differential equations is examined. …”
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Compact Implicit Integration Factor Method for the Nonlinear Dirac Equation by Jing-Jing Zhang, Xiang-Gui Li, Jing-Fang Shao

“…For the temporal discretization, the implicit integration factor method is applied to deal with the nonlinear system. We therefore develop two implicit integration factor numerical schemes with full discretization, one of which can achieve fourth-order accuracy in both space and time. …”
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The New Semianalytical Technique for the Solution of Fractional-Order Navier-Stokes Equation by Nehad Ali Shah, Mounirah Areshi, Jae Dong Chung, Kamsing Nonlaopon

“…Then, we apply this new method to analyze the fractional-order nonlinear system of Navier-Stokes models. Finally, we provide 3-D graphical plots to support the impact of the fractional derivative acting on the behavior of the obtained profile solutions to the suggested models.…”
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Newfangled Linearization Formula of Certain Nonsymmetric Jacobi Polynomials: Numerical Treatment of Nonlinear Fisher’s Equation by W. M. Abd-Elhameed, Afnan Ali, Y. H. Youssri

“…The presented method is used to convert the equation governed by its underlying conditions into a nonlinear system of equations. The solution of the resulting system can be obtained through any suitable standard numerical scheme. …”
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The Exact Linearization and LQR Control of Semiactive Connected Hydropneumatic Suspension System by Xuyang Cao, Linlin Cao, Dianlong Wang

“…Based on differential geometry theory, the nonlinear system of connected hydropneumatic suspension was transformed to a linear one. …”
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Identification of the boundary regime in the process of water-oil displacement from the reservoir by Gamzaev Khanlar

“…The water-oil displacement process (from a rectangular reservoir) has been considered, that is described by a nonlinear system of partial differential equations with respect to the reservoir pressure (RP) and displacing phase saturation (DPS). …”
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ROLLING BEARING WEAK FAULT FEATURE EXTRACTION BASED ON MULTIPOINT OPTIMAL MINIMUM ENTROY DECONVOLUTION ADJUSTED AND ADAPTIVE STOCHASTIC RESONANCE WITH CUCKOO SEARCH by QUAN ZhenYa, ZHANG XueLiang

“…Adjusting the value of nonlinear system parameters will affect the output Signal-to-Noise Ratio（ SNR）,so Signalto-Noise Ratio（ SNR） was used as the output evaluation index of stochastic resonance. …”
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