Image Encryption Algorithm Based on a Novel Improper Fractional-Order Attractor and a Wavelet Function Map by Jian-feng Zhao, Shu-ying Wang, Li-tao Zhang, Xiao-yan Wang

“…It is noted that the nonlinear characteristic of the improper fractional-order chaos is interesting. …”
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On the Limit Cycles for a Class of Perturbed Fifth-Order Autonomous Differential Equations by Nabil Sellami, Romaissa Mellal, Bahri Belkacem Cherif, Sahar Ahmed Idris

“…We study the limit cycles of the fifth-order differential equation x⋅⋅⋅⋅⋅−ex⃜−dx⃛−cx¨−bx˙−ax=εFx,x˙,x¨,x⋯,x⃜ with a=λμδ,b=−λμ+λδ+μδ,c=λ+μ+δ+λμδ,d=−1+λμ+λδ+μδ,e=λ+μ+δ, where ε is a small enough real parameter, λ,μ, and δ are real parameters, and F∈C2 is a nonlinear function. Using the averaging theory of first order, we provide sufficient conditions for the existence of limit cycles of this equation.…”
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Preventing Noise-Induced Extinction in Discrete Population Models by Irina Bashkirtseva

“…A problem of the analysis and prevention of noise-induced extinction in nonlinear population models is considered. For the solution of this problem, we suggest a general approach based on the stochastic sensitivity analysis. …”
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Viscosity Approximation Methods and Strong Convergence Theorems for the Fixed Point of Pseudocontractive and Monotone Mappings in Banach Spaces by Yan Tang

“…The results presented in this paper extend most of the results that have been proposed for this class of nonlinear mappings.…”
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Two-Dimensional and Axisymmetric Unsteady Flows due to Normally Expanding or Contracting Parallel Plates by Saeed Dinarvand, Abed Moradi

“…The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates for two cases, the two-dimensional flow case and the axisymmetric flow case, is investigated. The governing nonlinear equations and their associated boundary conditions are transformed into a highly non-linear ordinary differential equation. …”
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Fuzzy Lattice Reasoning for Pattern Classification Using a New Positive Valuation Function by Yazdan Jamshidi Khezeli, Hossein Nezamabadi-pour

“…In this work, we improve the performance of FLR classifier by defining a new nonlinear positive valuation function. As a consequence, the modified algorithm achieves better classification results. …”
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Solution of Second-Order IVP and BVP of Matrix Differential Models Using Matrix DTM by Reza Abazari, Adem Kılıcman

“…We introduce a matrix form of differential transformation method (DTM) and apply for nonlinear second-order initial value problems (IVPs) and boundary value problems (BVPs) of matrix models which are given by 𝐮(𝑡)=𝑓(𝑡,𝐮(𝑡),𝐮(𝑡)) and subject to initial conditions 𝐮(𝑎)=𝐮0,𝐮(𝑎)=𝐮1 and boundary conditions 𝐮(𝑎)=𝐮0,𝐮(𝑏)=𝐮1, where 𝐮0,𝐮1∈𝑅𝑟×𝑞. …”
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Exact Solutions of Travelling Wave Model via Dynamical System Method by Heng Wang, Longwei Chen, Hongjiang Liu

“…By using the method of dynamical system, the exact travelling wave solutions of the coupled nonlinear Schrödinger-Boussinesq equations are studied. …”
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Generalized Auto-Convolution Volterra Integral Equations: Numerical Treatments by Mahdi Namazi Nezamabadi, Saeed Pishbin

“…We also investigate solvability of the obtained nonlinear system with infinite dimensional space and examine the convergence analysis of this method under the L2− norm. …”
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Coiflet Wavelet-Homotopy Solution of Channel Flow due to Orthogonally Moving Porous Walls Governed by the Navier–Stokes Equations by Qing-Bo Chen, Hang Xu

“…A newly computational method based on the Coiflet wavelet and homotopy analysis method is developed, which inherits the great nonlinear treatment of the homotopy analysis technique and the local high-precision capability of the wavelet approach, to give solutions to the classic problem of channel flow with moving walls. …”
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M-Eigenvalues-Based Sufficient Conditions for the Positive Definiteness of Fourth-Order Partially Symmetric Tensors by Gang Wang, Linxuan Sun, Lixia Liu

“…M-eigenvalues of fourth-order partially symmetric tensors play important roles in the nonlinear elastic material analysis and the entanglement problem of quantum physics. …”
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Adaptive Moving Sliding Mode Control for SISO Systems: Application to an Electropneumatic System by Assil Ayadi, Soufien Hajji, Mohamed Smaoui, Abdessattar Chaari

“…This paper aims to propose and develop an adaptive moving sliding mode controller (AMSMC) that can be applied for nonlinear single-input single-output (SISO) systems with external disturbances. …”
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Nonoscillatory Central Schemes for Hyperbolic Systems of Conservation Laws in Three-Space Dimensions by Andrew N. Guarendi, Abhilash J. Chandy

“…Details of the schemes, their implementation, and properties are presented together with results from several prototypical applications of hyperbolic conservation laws including a nonlinear scalar equation, the Euler equations of gas dynamics, and the ideal magnetohydrodynamic equations. …”
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Novel extended multivariate public key cryptosystem by Shuai-ting QIAO, Yi-fa LI, Wen-bao HAN

“…To resist linearization attack and differential attack effectively, a nonlinear invertible transformation based on“tame transformation” was constructed. …”
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On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode-Dependent Delays by Xinghua Liu, Hongsheng Xi

“…The exponential stability of neutral Markovian jump systems with interval mode-dependent time-varying delays, nonlinear perturbations, and partially known transition rates is investigated. …”
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A Penalized-Equation-Based Generalized Newton Method for Solving Absolute-Value Linear Complementarity Problems by Yuan Li, Hai-Shan Han, Dan-Dan Yang

“…We propose a new approximation reformulation of absolute value linear complementarity problems by using a nonlinear penalized equation. Based on this approximation reformulation, a penalized-equation-based generalized Newton method is proposed for solving the absolute value linear complementary problem. …”
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Common Fixed Points of (α,η) − (θ,ϝ) Rational Contractions with Applications by Mujahid Abbas, Hira Iqbal, Manuel De La Sen

“…As application, we establish the existence of solutions of nonlinear elastic beam equations and first-order periodic problem.…”
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Monotone and Concave Positive Solutions to a Boundary Value Problem for Higher-Order Fractional Differential Equation by Jinhua Wang, Hongjun Xiang, Yuling Zhao

“…We consider boundary value problem for nonlinear fractional differential equation D0+αu(t)+f(t,u(t))=0,  0<t<1,  n-1<α≤n,  n>3,  u(0)=u'(1)=u′′(0)=⋯=u(n-1)(0)=0, where D0+α denotes the Caputo fractional derivative. …”
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Calculation of Wall Heat Conductivity under Non-Symmetric Boundary Conditions by R. I. Yesman

“…Advancing of phase transformation front along cross-section is considered with the purpose to take into account phase and chemical transformations in high-impact coatings and the Dirac δ-function is applied in this case.While stating a problem nonlinear boundary conditions and differential equations of heat transfer with due account of thermal and physical characteristics dependence on temperature have been used in the paper. …”
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A Conjugate Gradient Method with Global Convergence for Large-Scale Unconstrained Optimization Problems by Shengwei Yao, Xiwen Lu, Zengxin Wei

“…The conjugate gradient (CG) method has played a special role in solving large-scale nonlinear optimization problems due to the simplicity of their very low memory requirements. …”
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