Linear and Riccati matrix equations by Lloyd K. Williams

“…In this paper we find exact solutions for linear ordinary differential equations of any order when they are given in matrix form, as well as for classes of Riccati matrix equations with two or three arbitrary matrix coefficients. Other nonlinear systems of triangular form are also solved completely.…”
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Driven Force Induced Bifurcation Delay on the Chaotic Financial System by Balamurali Ramakrishnan, Mohamed Abdalla, Salah Boulaaras, Karthikeyan Rajagopal

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A New Fractional-Order Map with Infinite Number of Equilibria and Its Encryption Application by Ahlem Gasri, Amina-Aicha Khennaoui, Adel Ouannas, Giuseppe Grassi, Apostolos Iatropoulos, Lazaros Moysis, Christos Volos

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A Simple Chaotic Wien Bridge Oscillator with a Fractional-Order Memristor and Its Combination Synchronization for Efficient Antiattack Capability by Anitha Karthikeyan, Karthikeyan Rajagopal, Victor Kamdoum Tamba, Girma Adam, Ashokkumar Srinivasan

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Normal Forms for Nonautonomous Nonlinear Difference Systems Under Nonuniform Dichotomy Spectrum by Ning Song

“…In this paper, the normal forms of nonautonomous nonlinear systems with discrete time are investigated. …”
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Finite Difference Computation of Au-Cu/Magneto-Bio-Hybrid Nanofluid Flow in an Inclined Uneven Stenosis Artery by H. Thameem Basha, Karthikeyan Rajagopal, N. Ameer Ahammad, S. Sathish, Sreedhara Rao Gunakala

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A Multilayer Feed Forward Small-World Neural Network Controller and Its Application on Electrohydraulic Actuation System by Xiaohu Li, Feng Xu, Jinhua Zhang, Sunan Wang

“…Being difficult to attain the precise mathematical models, traditional control methods such as proportional integral (PI) and proportional integral differentiation (PID) cannot meet the demands for real time and robustness when applied in some nonlinear systems. The neural network controller is a good replacement to overcome these shortcomings. …”
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Exploring nonlinearity in quarter car models with an experimental approach to formulating fractional order form and its dynamic analysis by Tadios Molla, Prakash Duraisamy, Karthikeyan Rajagopal, Anitha Karthikeyan, Salah Boulaaras

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Decoupling the Stationary Navier-Stokes-Darcy System with the Beavers-Joseph-Saffman Interface Condition by Yong Cao, Yuchuan Chu, Xiaoming He, Mingzhen Wei

“…Newton iteration will be used to deal with the nonlinear systems. Numerical results are presented to illustrate the features of the proposed method.…”
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REALIZATION OF DISCRETE NONLINEAR DYNAMICAL SYSTEMS WITH CHAOTIC REGIMES BASED ON FIXED-POINT ARITHMETIC by U. A. Sychou

“…In this article, the problem of the practical realization of nonlinear systems with chaotic dynam-ics for targeted generation of chaotic sequences in digital devices is considered. …”
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On a New Reliable Algorithm by A. K. Alomari, M. S. M. Noorani, R. Nazar

“…Comparisons between the MSHAM solutions and the fourth-order Runge-Kutta (RK4) numerical solutions reveal that the new technique is a promising tool for the nonlinear systems of ordinary differential equations.…”
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Global Existence and Asymptotic Behavior of Solutions for Compressible Two-Fluid Euler–Maxwell Equation by Ismahan Binshati, Harumi Hattori

“…Moreover, we use the result for Lp−Lq estimates to prove the decay rates for the nonlinear systems.…”
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Fractional-Order Sliding Mode Synchronization for Fractional-Order Chaotic Systems by Chenhui Wang

“…Some sufficient conditions, which are valid for stability check of fractional-order nonlinear systems, are given in this paper. Based on these results, the synchronization of two fractional-order chaotic systems is investigated. …”
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Searching for Analytical Solutions of the (2+1)-Dimensional KP Equation by Two Different Systematic Methods by Yongyi Gu, Fanning Meng

“…The results demonstrate that the applied methods are efficient and direct methods to solve the complex nonlinear systems.…”
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Complexity in Linear Systems: A Chaotic Linear Operator on the Space of Odd 2π-Periodic Functions by Tamás Kalmár-Nagy, Márton Kiss

“…Not just nonlinear systems but infinite-dimensional linear systems can exhibit complex behavior. …”
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Characterization of Polymer Surfaces by the Use of Different Wetting Theories Regarding Acid-Base Properties by Eduard Kraus, Lukas Orf, Michael Heilig, Benjamin Baudrit, Irina Starostina, Oleg Stoyanov

“…Striving for a better understanding of the adhesive polymer interactions in adhesively joined polymers, the methods of Berger and van Oss-Chaudhury-Good were found as the most suitable methods for the investigation of wetting on solid polymer surfaces. Methods of nonlinear systems by Della Volpe and Siboni were adapted and evaluated on plastic surfaces. …”
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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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Adaptive Fuzzy Tracking Control for a Class of Uncertain Nonlinear Time-Delayed Systems with Saturation Constrains by Yu-Jun Zhang, Li-Bing Wu, Hong-Yang Zhao, Xiao-Dong Hu, Wen-Yu Zhang, Dong-Ying Ju

“…In this paper, the problem of adaptive fuzzy tracking control is considered for a class of uncertain nonaffine nonlinear systems with external disturbances, multiple time delays, and nonsymmetric saturation constrains. …”
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Pulse Width Modulation Control of Mecanum-Wheeled Mobile Robot With Random Noise by Ruijie Yin, Zhaojing Wu, Likang Feng

“…As a preliminary, PWM strategy of random nonlinear systems is obtained by the aid of the functional analysis tool. …”
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Impulsive Control and Synchronization of Complex Lorenz Systems by Shaban Aly, Ali Al-Qahtani, Houari B. Khenous, Gamal M. Mahmoud

“…In this paper, we continue our investigations on control and synchronization of the complex Lorenz systems by investigating impulsive control and synchronization. Nonlinear systems involving impulse effects, appear as a natural description of observed evolution phenomena of several real world problems; For example, many biological phenomena involving thresholds, bursting rhythm models in medicine and biology, optimal control models in economics, population dynamics and so forth do exhibit impulsive effects. …”
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