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Nonlinearity

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  • This volume covers a diverse collection of topics dealing with some of the fundamental concepts and applications embodied in the study of nonlinear dynamics. Each of the 15 chapters contained in this compendium generally fit into one of five topical areas: physics applications, nonlinear oscillators, electrical and mechanical systems, biological and behavioral applications or random processes. The authors of these chapters have contributed a stimulating cross section of new results, which provide a fertile spectrum of ideas that will inspire both seasoned researches and students....

    pdf374p 123859674 30-06-2012 65 17   Download

  • All practical systems contain nonlinear dynamics. Control system development for these systems has traditionally been based on linearized system dynamics in conjunction with linear control techniques. Sometimes it is possible to describe the operation of systems by a linear model around its operating points. Linearized system can provide approximate behavior of the system. But in analyzing the overall system behavior, the resulting system model is inadequate or inaccurate. Moreover, the stability of the system cannot be guaranteed.

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  • Rapid development of optoelectronic devices and laser techniques poses an important task of creating and studying, from one side, the structures capable of effectively converting, modulating, and recording optical data in a wide range of radiation energy densities and frequencies, from another side, the new schemes and approaches capable to activate and simulate the modern features. It is well known that nonlinear optical phenomena and nonlinear optical materials have the promising place to resolve these complicated technical tasks....

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  • The book is intended to provide an introduction to the effects of nonlinear elements in feedback control systems. A central topic is the use of the Describing Function (DF) method since in combination with simulation it provides an excellent approach for the practicing engineer and follows on logically from a first course in classical control, such as the companion volume in this series. Some of the basic material on the topic can be found in my earlier book which is frequently referenced throughout the text....

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  • This article is concerned with local well-posedness of the Cauchy problem for second order quasilinear hyperbolic equations with rough initial data. The new results obtained here are sharp in low dimension. 1. Introduction 1.1. The results. We consider in this paper second order, nonlinear hyperbolic equations of the form (1.1) gij (u) ∂i ∂j u = q ij (u) ∂i u ∂j u on R × Rn , with Cauchy data prescribed at time 0, (1.2) u(0, x) = u0 (x) , ∂0 u(0, x) = u1 (x) .

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  • This lecture will teach you how to fit nonlinear functions by using bases functions and how to control model complexity. The goal is for you to: Learn how to derive ridge regression; understand the trade-off of fitting the data and regularizing it; Learn polynomial regression; understand that, if basis functions are given, the problem of learning the parameters is still linear; learn cross-validation; understand model complexity and generalization.

    pdf28p allbymyself_08 22-02-2016 31 4   Download

  • This paper focuses on mining the hyponymy (or is-a) relation from large-scale, open-domain web documents. A nonlinear probabilistic model is exploited to model the correlation between sentences in the aggregation of pattern matching results. Based on the model, we design a set of evidence combination and propagation algorithms.

    pdf10p hongdo_1 12-04-2013 39 2   Download

  • The aim of the dissertation is study and propose a new algorithm for solving the optimal problem in nonlinear model predictive control MIMO system.

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  • This chapter presents the following content: Linear versus nonlinear adjustment, simple extensions of the ARMA model, testing for nonlinearity, threshold autoregressive models, extensions of the TAR model, three threshold models, smooth transition models,...

    ppt62p nomoney17 04-07-2017 57 1   Download

  • This paper deals with the problem of asymptotic stability for a class of nonlinear discrete-time systems with time-varying delay. The time-varying delay is assumed to be belong to a given interval, in which the lower bound of delay is not restricted to zero. A linear matrix inequality (LMI) approach to asymptotic stability of the system is presented. Based on constructing improved Lyapunov functionals, delay-depenent criteria for the asymptotic stability of the system are established via linear matrix inequalities. A numerical example is given to show the effectiveness of the result..

    pdf5p vision1234 30-06-2018 12 1   Download

  • The paper proposes a nonlinear control method, which can be applied to output tracking control a wide range of various perturbed nonlinear objects. This output feedback controller is established based on piecewise quadratic optimizing subjected to input constraints for state feedback control and then combined with an appropriate EKF or UKF for system state observation.

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  • In this paper we study a boundary value problem for a nonlinear biharmonic equation, which models a bending plate on nonlinear elastic foundation. We propose a new approach to existence and uniqueness and numerical solution of the problem.

    pdf17p thuyliebe 05-10-2018 19 0   Download

  • In this paper we review our works in the field of nonlinear optics in waveguide arrays (WAs) and photonic nanowires. We first focus on the new equation governing light propagation in optical fibers with sub-wavelength cores which simultaneously takes into account (i) the vector nature of the electromagnetic modes inside fibers, (ii) the strong dispersion of the nonlinearity inside the spectral body of the pulse, (iii) and the full variations of the vector mode profiles with frequency.

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  • In this paper, we will consider a nonlinear system with random telegraph noises in a Raman ring laser by modeling the laser pump light as a pre-Gaussian process and find an exactly soluble equation for the stationary probability distribution of fluctuations in this nonlinear system under the influence of two-telegraph noise.

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  • In this paper, a general propagation equation of ultrashort pulses in an arbitrary dispersive nonlinear medium has been used for the case of Kerr media. This equation which is called Generalized Nonlinear Schroedinger Equation usually has very complicated form and looking for its solutions is usually a very difficult task. Theoretical methods reviewed in this paper to solve this equation are effective only for some special cases.

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  • Using density-matrix theory, an analytical expression of the self-Kerr nonlinear coefficient of a three-level lambda EIT medium for a weak probe light is derived. Influences of the coupling light and Doppler broadening on the self-Kerr coefficient are investigated and compared to experimental observation with a good agreement. The selfKerr nonlinearity of the medium is modified and greatly enhanced in the spectral region of EIT window.

    pdf8p thuyliebe 09-10-2018 12 0   Download

  • This paper presents a displacement - based finite element formulation for nonlinear analysis of steel - concrete composite planar frames subjected to combined action of gravity and lateral loads. A 6DOF super element is proposed for modelling composite beam, allowing for partial interaction between the steel beam and the concrete slab, semi - rigid nature of beam to column composite connection and material nonlinearity.

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  • The paper provides a new view on the averaging procedure and equivalent linearization in the study of nonlinear mechanics. It is shown that the duality of those techniques can be used to obtain better approximate solutions or to separate the original nonlinear systems subjected to periodic and random excitations into deterministic and stochastic ones.

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  • . In this paper an approximate analytical solution to analyze the nonlinear buckling and postbuckling behavior of imperfect functionally graded panels with the Poisson’s ratio also varying smoothly along the thickness is investigated. Based on the classical shell theory and von Karman’s assumption of kinematic nonlinearity and applying Galerkin procedure, the equations for finding critical loads and load-deflection curves of cylindrical panel subjected to axial compressive load with two types boundary conditions, are given.

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  • In this short communication the main ideas of the method of equivalent linearization and dual conception are further extended to suggest a new technique for solving nonlinear differential equations. This technique allows improving the accuracy when the nonlinearity is strong and getting nonlinear features of responses. For illustration the Duffing oscillator is considered to demonstrate the effectiveness of the proposed technique.

    pdf4p thienthanquydu 17-10-2018 19 0   Download

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