The Discrete Ueda System and Its Fractional Order Version: Chaos, Stabilization and Synchronization by Louiza Diabi, Adel Ouannas, Amel Hioual, Giuseppe Grassi, Shaher Momani

“…The Ueda oscillator is one of the most popular and studied nonlinear oscillators. Whenever subjected to external periodic excitation, it exhibits a fascinating array of nonlinear behaviors, including chaos. …”
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Algorithms for Solving the Equilibrium Composition Model of Arc Plasma by Zhongyuan Chi, Yuzhang Ji, Ningning Liu, Tianchi Jiang, Xin Liu, Weijun Zhang

“…This model is essentially a nonlinear system of weakly singular Jacobian matrices. …”
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A Competitive Swarm Optimizer-Based Technoeconomic Optimization with Appliance Scheduling in Domestic PV-Battery Hybrid Systems by Bo Wang, Yanjing Li, Fei Yang, Xiaohua Xia

“…To solve the proposed mixed-integer nonlinear programming problem at a large scale, a competitive swarm optimizer-based numerical solver is designed and employed. …”
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Convergence of a Two-Step Iterative Method for Nondifferentiable Operators in Banach Spaces by Abhimanyu Kumar, Dharmendra K. Gupta, Eulalia Martínez, Sukhjit Singh

“…The semilocal and local convergence analyses of a two-step iterative method for nonlinear nondifferentiable operators are described in Banach spaces. …”
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New Rational Homoclinic and Rogue Waves for Davey-Stewartson Equation by Changfu Liu, Chuanjian Wang, Zhengde Dai, Jun Liu

“…This result shows that rogue wave can be generated by extreme behavior of homoclinic breather wave for higher dimensional nonlinear wave fields.…”
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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). …”
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Controllability of Neutral Fractional Functional Equations with Impulses and Infinite Delay by R. Ganesh, R. Sakthivel, Yong Ren, S. M. Anthoni, N. I. Mahmudov

“…More precisely, a set of sufficient conditions are derived for the exact controllability of nonlinear neutral impulsive fractional functional equation with infinite delay. …”
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Dynamical Analysis and Control of a Chaotic Microelectromechanical Resonator Model by Dailhane G. Bassinello, Angelo M. Tusset, Rodrigo T. Rocha, Jose M. Balthazar

“…The dynamic analysis and control of a nonlinear MEM resonator system are considered. Phase diagram, bifurcation diagram, and the 0-1 test are applied to the analysis of the influence of the parameters on the dynamics of the system, whose parameters are damping coefficient, polarization of the voltage, and nonlinear stiffness term. …”
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Extended and Unscented Kalman Filtering Applied to a Flexible-Joint Robot with Jerk Estimation by Mohammad Ali Badamchizadeh, Iraj Hassanzadeh, Mehdi Abedinpour Fallah

“…Robust nonlinear control of flexible-joint robots requires that the link position, velocity, acceleration, and jerk be available. …”
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Exponential Stability of Switched Positive Homogeneous Systems by Dadong Tian, Shutang Liu

“…This paper studies the exponential stability of switched positive nonlinear systems defined by cooperative and homogeneous vector fields. …”
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Determination of Damage in Reinforced Concrete Frames with Shear Walls Using Self-Organizing Feature Map by Mehdi Nikoo, Łukasz Sadowski, Faezehossadat Khademi, Mohammad Nikoo

“…The obtained model was compared with linear regression (LR) and nonlinear regression (NonLR) models and also the radial basis function (RBF) of a neural network. …”
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Newton Method to Recover the Phase Accumulated during MRI Data Acquisition by Oh-In Kwon, Chunjae Park

“…In this study, we estimate the magnetic flux density, which is recoverable from nonlinearly encoded MR k-space data by applying a Newton method.…”
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Optimal Sixteenth Order Convergent Method Based on Quasi-Hermite Interpolation for Computing Roots by Fiza Zafar, Nawab Hussain, Zirwah Fatimah, Athar Kharal

“…We have given a four-step, multipoint iterative method without memory for solving nonlinear equations. The method is constructed by using quasi-Hermite interpolation and has order of convergence sixteen. …”
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Spherical Simplex-Radial Cubature Quadrature Kalman Filter by Zhaoming Li, Wenge Yang

“…A spherical simplex-radial cubature quadrature Kalman filter (SSRCQKF) is proposed in order to further improve the nonlinear filtering accuracy. The Gaussian probability weighted integral of the nonlinear function is decomposed into spherical integral and radial integral, which are approximated by spherical simplex cubature rule and arbitrary order Gauss-Laguerre quadrature rule, respectively, and the novel spherical simplex-radial cubature quadrature rule is obtained. …”
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Vibration of the Duffing Oscillator: Effect of Fractional Damping by Marek Borowiec, Grzegorz Litak, Arkadiusz Syta

“…We have applied the Melnikov criterion to examine a global homoclinic bifurcation and transition to chaos in a case of the Duffing system with nonlinear fractional damping and external excitation. …”
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Adaptive Neural Networks Synchronization of a Four-Dimensional Energy Resource Stochastic System by Duo Meng

“…Assuming the response system contains unknown uncertain nonlinearities and unknown stochastic disturbances, the neural networks and robust terms are used to identify the nonlinearities and overcome the stochastic disturbances, respectively. …”
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Linearization: Geometric, Complex, and Conditional by Asghar Qadir

“…Lie symmetry analysis provides a systematic method of obtaining exact solutions of nonlinear (systems of) differential equations, whether partial or ordinary. …”
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Hybrid Algorithm for Common Fixed Points of Uniformly Closed Countable Families of Hemirelatively Nonexpansive Mappings and Applications by Sumei Ai, Yongfu Su

“…The authors have obtained the following results: (1) the definition of uniformly closed countable family of nonlinear mappings, (2) strong convergence theorem by the monotone hybrid algorithm for two countable families of hemirelatively nonexpansive mappings in a Banach space with new method of proof, (3) two examples of uniformly closed countable families of nonlinear mappings and applications, (4) an example which is hemirelatively nonexpansive mapping but not weak relatively nonexpansive mapping, and (5) an example which is weak relatively nonexpansive mapping but not relatively nonexpansive mapping. …”
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Traveling Wave Solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony Equation by Zhengyong Ouyang

“…The results imply that we can deduce bell-shaped waves from periodic waves for some nonlinear evolution equations.…”
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Traveling Wave Solutions of Space-Time Fractional Generalized Fifth-Order KdV Equation by Dianchen Lu, Chen Yue, Muhammad Arshad

“…At the end, three types of exact traveling wave solutions are obtained which indicate that the method is very practical and suitable for solving nonlinear fractional partial differential equations.…”
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