Controllability of a fluid-structure interaction system coupling the Navier–Stokes system and a damped beam equation by Buffe, Rémi, Takahashi, Takéo

“…Then, the result on the nonlinear system is obtained by a fixed-point argument.…”
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The Dynamical Behavior of a Rigid Body Relative Equilibrium Position by T. S. Amer

“…The governing equations of motion are obtained using Lagrange’s equations and represent a nonlinear system of second-order differential equations that can be solved in terms of generalized coordinates. …”
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Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions by Mısır J. Mardanov, Yagub A. Sharifov, Kamala E. Ismayilova

“…Sufficient conditions are found for the existence and uniqueness of solutions for the boundary value problems for the first order nonlinear system of the impulsive ordinary differential equations with three-point boundary conditions. …”
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New Fractional Derivative Expression of the Shifted Third-Kind Chebyshev Polynomials: Application to a Type of Nonlinear Fractional Pantograph Differential Equations by Y. H. Youssri, W. M. Abd-Elhameed, H. M. Ahmed

“…The role of the tau method is to convert the pantograph differential equation with its governing initial/boundary conditions into a nonlinear system of algebraic equations that can be treated with the aid of Newton’s iterative scheme. …”
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Buckling suppression of a cantilever structure with a modified fuzzy sliding mode control by Jianhua Pan, Lin Sun, Xiaopei Liu, Yuyuan Zhang, Yili Duo

“…Subsequently, a second-order Galerkin discretization is applied to establish a two-dimensional nonlinear system for the cantilever structure. Numerical simulations demonstrate that a two-dimensional nonlinear dynamic model of the laminated composite structure is essential for precise buckling vibration estimations. …”
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Solving a system of nonlinear difference equations with bilinear dynamics by Hashem Althagafi, Ahmed Ghezal

“…This paper presented a comprehensive study of a three-dimensional nonlinear system of difference equations, which can be reduced to a two-dimensional bilinear system. …”
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Nonlinear versus Ordinary Adaptive Control of Continuous Stirred-Tank Reactor by Jiri Vojtesek, Petr Dostal

“…Proposed controller is tested by the simulations on the mathematical model of the continuous stirred-tank reactor with cooling in the jacket as a typical nonlinear system.…”
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Theoretical and Experimental Study on Rapid Decompression Oscillation in Altitude Chamber by Zifeng Tian, Jianfeng Lu, Zhao Gu, Lihua Yu, Hao Zhou, Lijun Yang

“…Given the frequent airflow excitation phenomenon caused by the rapid decompression of the altitude chamber, the mathematical model of the nonlinear system of the rapid decompression of the altitude chamber is established. …”
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Fault Feature Extraction of Gear Crack based on QPSO-Volterra by Chen Li, Xiaojuan Wei, Ningzhou Li

“…In view of the limitation of current mainstream methods of gear crack fault detection (that is only using the system response as research object, and seldom considering the input effect on fault feature extraction), and taking into account its dynamic characteristics as a kind of typical nonlinear system, by applying Volterra series theory into different states of gear meshing transmission system, for fully taking the advantage of Volterra series, which can use both the input and output data of system to describe the nonlinear characteristics of system. …”
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An Integrated Test-Based Nonlinear Aeroelastic Analysis Method to Freeplay-Induced Limit-Cycle Oscillations by Yukai Sun, Zhigang Wu, Chao Yang, Xiangyu Wang, Chuansheng Wang

“…An integrated nonlinear aeroelastic analysis method and procedure based on the nonlinear system identification technology is proposed. …”
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Extended Ellipsoidal Outer-Bounding Set-Membership Estimation for Nonlinear Discrete-Time Systems with Unknown-but-Bounded Disturbances by Yushuang Liu, Yan Zhao, Falin Wu

“…It has been demonstrated that the EEOB-SME algorithm is stable and the estimation errors of the EEOB-SME are bounded when the nonlinear system is observable. The EEOB-SME decreases the computation load and the feasible sets of EEOB-SME contain more true states. …”
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Control of Energy Storage Systems for Aeronautic Applications by G. Canciello, A. Cavallo, B. Guida

“…Formal stability proofs are given for the resulting nonlinear system, and strong robustness results from the use of high-gain and variable structure control implementation. …”
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Dissipative Filter Design for Nonlinear Time-Varying-Delay Singular Systems against Deception Attacks by Guobao Liu, Shibin Shen, Xianglei Jia

“…The validity of our work is illustrated through a mostly used example of the nonlinear system.…”
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Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model by Fabien Crauste

“…We analyze the asymptotic stability of a nonlinear system of two differential equations with delay,describing the dynamics of blood cell production. …”
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Function Projective Synchronization of Two Complex Networks with Unknown Sector Nonlinear Input and Multiple Time-Varying Delay Couplings by Na Fang, Da Wei, Nan-nan Yin, Dan-ying Xu, Hua Liu, Jie Fang

“…Different from some existing studies on nonlinear system with sector nonlinear input, this paper studies the synchronization of two complex dynamic networks when the boundary of sector nonlinear input is unknown. …”
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Generalized Quadratic Linearization of Machine Models by Parvathy Ayalur Krishnamoorthy, Kamaraj Vijayarajan, Devanathan Rajagopalan

“…In the exact linearization of involutive nonlinear system models, the issue of singularity needs to be addressed in practical applications. …”
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Implementing the Vieta–Lucas Collocation Optimization Method for MHD Casson and Williamson Model under the Effects of Heat Generation and Viscous Dissipation by M.M. Khader, A. Eid, M. Adel

“…This method is used to convert the problem’s system of ordinary differential equations (ODEs) into a nonlinear system of algebraic equations. This system is built as a restricted optimization problem and optimized to obtain the series solution’s unknown coefficients. …”
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Identification of Industrial Furnace Temperature for Sintering Process in Nuclear Fuel Fabrication Using NARX Neural Networks by Dede Sutarya, Benyamin Kusumoputro

“…Nonlinear system identification is becoming an important tool which can be used to improve control performance and achieve robust fault-tolerant behavior. …”
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Study on Dynamic Characteristics and Parameter Influence of a Kind of Bilateral Restraint Impact Vibration System by Li Ding, Shangshang Cheng, Kaifei Zhang, Jiajun Chai, He Li, Chengdong Niu, Chao Cao

“…With the help of the method of nonlinear system dynamics analysis research, the Poincaré mapping of hinge joint collision vibration is constructed, the bifurcation diagram of the system with different parameters is solved, and the variation law of the system motion and the influence of parameters are analyzed by combining the time response diagram, phase diagram, Poincaré cross section diagram, and spectrum diagram of the typical motion of the system. …”
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Multiple Model Adaptive Tracking Control Based on Adaptive Dynamic Programming by Kang Wang, Xiaoli Li, Yang Li

“…Adaptive dynamic programming (ADP) has been tested as an effective method for optimal control of nonlinear system. However, as the structure of ADP requires control input to satisfy the initial admissible control condition, the control performance may be deteriorated due to abrupt parameter change or system failure. …”
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