Turing patterns in a networked vegetation model by Xiaomei Bao, Canrong Tian

“…The parameter space of Turing patterns for plant behavior is obtained based on the analysis of the eigenvalues of the Laplacian of weighted graph, while the amplitude equation determining the stability of Turing patterns is obtained by weakly nonlinear analysis. We also show that the optimal rainfall is only determined by the density of the water. …”
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On the Analyticity for the Generalized Quadratic Derivative Complex Ginzburg-Landau Equation by Chunyan Huang

“…The strategy is to develop uniform and dyadic exponential decay estimates for the generalized Ginzburg-Landau semigroup e-a+it-Δα to overcome the derivative in the nonlinear term.…”
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A Modified Hybrid Conjugate Gradient Method for Unconstrained Optimization by Minglei Fang, Min Wang, Min Sun, Rong Chen

“…The nonlinear conjugate gradient algorithms are a very effective way in solving large-scale unconstrained optimization problems. …”
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Dynamic Analyses of Isolated Structures under Bi-Directional Excitations of Near-Field Ground Motions by Gokhan Ozdemir, Ugurhan Akyuz

“…Nonlinear response history analyses (NRHA) of a 3-story isolated reinforced concrete (RC) building are carried out under both uni- and bi-directional earthquake excitations of near-field records. …”
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Variational Iteration Method of Dropping Shock Response for the Suspension Spring Packaging System by Shuang Song, An-Jun Chen

“…In accordance with dropping shock dimensionless cubic nonlinear dynamic equation of suspension spring system, by variational iteration method, a first-order approximate solution of the system was obtained. …”
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Approximate Controllability of Semilinear Control System Using Tikhonov Regularization by Ravinder Katta, N. Sukavanam

“…We exhibit a sequence of regularized controls which steers the semilinear control system from an arbitrary initial state x0 to an ϵ neighbourhood of the target state xτ at time τ>0 under the assumption that the nonlinear function f is Lipschitz continuous. The convergence of the sequences of regularized controls and the corresponding mild solutions are shown under some assumptions on the system operators. …”
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Global Dynamics of Rational Difference Equations xn+1=xn+xn-1/q+ynyn-1 and yn+1=yn+yn-1/p+xnxn-1 by Keying Liu, Peng Li, Weizhou Zhong

“…Global dynamics of a system of nonlinear difference equations was investigated, which had five kinds of equilibria including isolated points and a continuum of nonhyperbolic equilibria along the coordinate axes. …”
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Numerical Solution of Piecewise Constant Delay Systems Based on a Hybrid Framework by H. R. Marzban, S. Hajiabdolrahmani

“…It is shown that the developed approach is also applicable to a special class of nonlinear piecewise constant delay differential equations. …”
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BOLT COUPLING STRUCTURE OF CONTACT STRESS AND THE INFLUENCE FACTORS OF JOINT STIFFNESS by YANG Hui, HAN Jiang, CHU XiangQian

“…Considering the nonlinear factors,the contact and friction between plates as well as bolt and plates,bolt preload,etc,three-dimensional finite element model bolted structure was developed. …”
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Solutions of Stiff Systems of Ordinary Differential Equations Using Residual Power Series Method by Mubashir Qayyum, Qursam Fatima

“…RPSM is applied to various linear and nonlinear stiff systems, and closed-form solutions are achieved. …”
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Geometric Meshing Simulation Analysis of Zero Spiral Bevel Gear by Zhou Jiaojun

“…The contact path and transmission error curve are obtained by solving the nonlinear equations system. Then,the major axis of instantaneous contact ellipse is calculated based on differential geometry. …”
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Analytic Approximate Solution for Falkner-Skan Equation by Vasile Marinca, Remus-Daniel Ene, Bogdan Marinca

“…This paper deals with the Falkner-Skan nonlinear differential equation. An analytic approximate technique, namely, optimal homotopy asymptotic method (OHAM), is employed to propose a procedure to solve a boundary-layer problem. …”
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Topological Quasilinear Spaces by Yılmaz Yılmaz, Sümeyye Çakan, Şahika Aytekin

“…He introduced a kind of the concept of a quasilinear spaces both including a classical linear spaces and also nonlinear spaces of subsets and multivalued mappings. …”
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Line Spectrum Chaotification on QZS Systems with Time-Delay Control by Jing Zhang, Tao Tang, Wenhua Fang

“…Thus, an isolation raft system based on quasi-zero-stiffness (QZS) property is proposed for line spectrum chaotification. A nonlinear time-delay controller is derived accordingly. …”
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A SVM Based Spectrum Prediction Scheme for Cognitive Radio by Yuan Xu, Huaxiang Lu, Xu Chen

“…The channel status is forecasted by utilizing the excellent forecasting performance of the model in small sample and nonlinear data of SVM. The results show that by avoiding invalid prediction, the spectrum utilization can also be improved, and the forecasting accuracy is better than model based on back propagation（BP）, thus the proposed algorithm is practicable and flexible for spectrum prediction in cognitive radio.…”
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A Mixed Traffic Assignment Problem and Its Upper Bound of Efficiency Loss by Xiao-Jun Yu, Jiancheng Long

“…The users governed by the UE player use the paths with minimum actual travel cost, while the users governed by altruistic players use the paths with minimum perceived travel cost, which is a linear combination of the actual and marginal travel costs. A nonlinear programming method is adopted to derive the efficiency loss of the UE-AP mixed equilibrium with polynomial cost function. …”
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Representation of Manifolds for the Stochastic Swift-Hohenberg Equation with Multiplicative Noise by Yanfeng Guo, Donglong Li

“…The approximate parameterizations of the small scales for the large scales are given in the process of seeking for stochastic parameterizing manifolds, which are obtained as pullback limits of some backward-forward systems depending on the time-history of the dynamics of the low modes in a mean square sense through the nonlinear terms. When the corresponding pullback limits of some backward-forward systems are efficiently determined, the corresponding non-Markovian reduced systems can be obtained for researching good modeling performances in practice.…”
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FAULT DIAGNOSIS OF RECIPROCATING COMPRESSOR ON THE RESONANCE-BASED SPARSE SIGNAL DECOMPOSITION WITH OPTIMAL Q-FACTOR by WANG JinDong, BU QingChao, ZHAO HaiYang, ZHANG HongBin

“…Reciprocating compressor vibration signal is typical nonlinear and non-stationary,and the vibration information interference coupling, owing to this problem,a fault diagnosis method of reciprocating compressor on the resonance-based sparse signal decomposition with optimal Q-factor was proposed.The method use resonance sparse decomposition to find the low resonance component which its kurtosis is maximum, optimize Q-factor with genetic algorithm and particle swarm optimization to get the optimal Q-factor;then use resonance sparse decomposition to decompose reciprocating compressor vibration signal by the optimal Q-factor;the result shows that this method can diagnose the oversized bearing clearance fault effectively.…”
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From the Guest Editors by Urszula Ledzewicz, Andrzej Swierniak

“…The idea for this volume came from the session ''Control and Dynamics ofBiomedical Systems,'' which we organized at the Fourth World Congress of NonlinearAnalysts held in Orlando, Florida, on June 30–July 7, 2004. …”
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Least Square Homotopy Perturbation Method for Ordinary Differential Equations by Mubashir Qayyum, Imbsat Oscar

“…The proposed scheme is tested against various linear and nonlinear BVPs (second to seventh order DEs). Validity of the obtained solutions is confirmed by finding absolute errors. …”
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