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). …”
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Chaotic Dynamics Analysis Based on Financial Time Series by Zheng Gu, Yuhua Xu

“…Secondly, the dynamic system of some nonlinear characteristic data is established according to the Taylor series expansion form, and the corresponding dynamic characteristics are analyzed. …”
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Existence Results for ψ-Hilfer Fractional Integro-Differential Hybrid Boundary Value Problems for Differential Equations and Inclusions by Chanakarn Kiataramkul, Sotiris K. Ntouyas, Jessada Tariboon

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An insight into the stochastic solitonic features of the Maccari model using the solver technique. by Hesham G Abdelwahed, Reem Alotaibi, Emad K El-Shewy, Mahmoud A E Abdelrahman

“…In this paper, the unified approach is used in acquiring some new results to the coupled Maccari system (MS) in Itô sense with multiplicative noise. The MS is a nonlinear model used in hydrodynamics, plasma physics, and nonlinear optics to represent isolated waves in a restricted region. …”
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Optical leptons by Lubomir M. Kovachev

“…We obtain optical vortices with classical orbital momentum ℓ=1 and spin j=±1/2 as exact solutions of a system of nonlinear Maxwell equations (NMEs). Two kinds of Kerr-type media, namely, those with and without linear dispersion of the electric and the magnet susceptibility, are investigated. …”
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Steady-State Fuzzy Modeling of Ultrasonic Motor System by Shi Jingzhuo, Lv Lin

“…Because of the complicated energy conversion process, ultrasonic motor has remarkable nonlinearity. Therefore, it is difficult to achieve accurate speed control of ultrasonic motor. …”
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Extending locked range of digital phase-locked loop by prediction estimation of states by ZHAO Yi-bo1, LUO Xiao-shu2, ZHANG Dao-yang3, FENG Jiu-chao1

“…A method to extend locked range of the positive zero crossing detection digital phase-locked loop（ZC-DPLL） was proposed.The nonlinear dynamical model of phase error of a non-controlled DPLL is firstly built,linearation predic-tion estimation of phase error in the stationary point domain is derived.Then nonlinear function of this prediction estima-tion is used to control by feedback.Locked range of the phase-locked loop is extended.Stability of fixed point of the controlled system is analyzed and the results by simulation are given.The effects not only show the proposed method is correct and effective but also it is superior to delay feedback method.…”
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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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Epidemic models with differential susceptibility and stagedprogression and their dynamics by James M. Hyman, Jia Li

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Feedback Control Method Using Haar Wavelet Operational Matrices for Solving Optimal Control Problems by Waleeda Swaidan, Amran Hussin

“…The proposed method has been applied to solve linear and nonlinear optimal control problems with infinite time horizon. …”
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Synchronization of Coupled Networks with Uncertainties by Yi Zuo, Xinsong Yang

“…A distinct feature of the network is that all the dynamical nodes are affected by uncertain nonlinear nonidentical perturbations. In order to synchronize the network onto a given isolate trajectory, a novel adaptive controller is designed to overcome the effects of the nonidentical uncertain nonlinear perturbations. …”
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Functional differential equations with infinite delay in Banach spaces by Jin Liang, Tijun Xiao

“…Moreover, we discuss the relation between the exponential asymptotic stability of the zero solution of nonlinear functional differential equation with infinite delay in a Banach space and the exponential stability of the solution semigroup of the corresponding linear equation, and find that the exponential stability problem of the zero solution for the nonlinear equation can be discussed only in the exponentially fading memory phase space.…”
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Chebyshev Wavelet Finite Difference Method: A New Approach for Solving Initial and Boundary Value Problems of Fractional Order by A. Kazemi Nasab, A. Kılıçman, Z. Pashazadeh Atabakan, S. Abbasbandy

“…A new method based on a hybrid of Chebyshev wavelets and finite difference methods is introduced for solving linear and nonlinear fractional differential equations. The useful properties of the Chebyshev wavelets and finite difference method are utilized to reduce the computation of the problem to a set of linear or nonlinear algebraic equations. …”
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A Spherically Symmetric Model for the Tumor Growth by Saeed M. Ali, Ashfaque H. Bokhari, M. Yousuf, F. D. Zaman

“…The nonlinear tumor equation in spherical coordinates assuming that both the diffusivity and the killing rate are functions of concentration of tumor cell is studied. …”
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Positive Solutions for a Class of Third-Order Three-Point Boundary Value Problem by Xiaojie Lin, Zhengmin Fu

“…We investigate the problem of existence of positive solutions for the nonlinear third-order three-point boundary value problem u‴(t)+λa(t)f(u(t))=0, 0<t<1, u(0)=u′(0)=0, u″(1)=∝u″(η), where λ is a positive parameter, ∝∈(0,1), η∈(0,1), f:(0,∞)→(0,∞), a:(0,1)→(0,∞) are continuous. …”
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Analysis of the Fractional-Order Kaup–Kupershmidt Equation via Novel Transforms by Naveed Iqbal, Humaira Yasmin, Ali Rezaiguia, Jeevan Kafle, A. Othman Almatroud, Taher S. Hassan

“…This technique is a mixture of the novel integral transformation Elzaki transformation and the new iteration technique. The nonlinear term can be handled easily by a new iteration technique. …”
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The Improved Generalized tanh-coth Method Applied to Sixth-Order Solitary Wave Equation by M. Torvattanabun, J. Simmapim, D. Saennuad, T. Somaumchan

“…The improved generalized tanh-coth method is used in nonlinear sixth-order solitary wave equation. This method is a powerful and advantageous mathematical tool for establishing abundant new traveling wave solutions of nonlinear partial differential equations. …”
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INCREMENTAL HARMONIC BALANCE METHOD FOR THE STUDY OF SUPPORT LOOSENESS FAULT’S CHARACTERISTICS by CAO QingSong, XIANG Qin, XIONG GuoLiang

“…Incremental harmonic balance method was exploited to solve the nonlinear equation,and iterative algorithm was applied to gain the vibration periodic solution. …”
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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

“…Oscillators with piecewise nonlinear characteristics are taken as illustrative examples. …”
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Higher-Order Multifractal Detrended Partial Cross-Correlation Analysis for the Correlation Estimator by Keqiang Dong, Xiaojie Gao

“…In this paper, we develop a new method to measure the nonlinear interactions between nonstationary time series based on the detrended cross-correlation coefficient analysis. …”
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