Search results for "Nonlinear system"
showing 10 items of 1446 documents
Pairs of nontrivial smooth solutions for nonlinear Neumann problems
2020
Abstract We consider a nonlinear Neumann problem driven by a nonhomogeneous differential operator with a reaction term that exhibits strong resonance at infinity. Using variational tools based on the critical point theory, we prove the existence of two nontrivial smooth solutions.
Deformations of third-order Peregrine breather solutions of the nonlinear Schrödinger equation with four parameters
2013
We present a new representation of solutions of the one-dimensional nonlinear focusing Schr\"odinger equation (NLS) as a quotient of two determinants. This formulation gives in the case of the order 3, new solutions with four parameters. This gives a very efficient procedure to construct families of quasirational solutions of the NLS equation and to describe the apparition of multirogue waves. With this method, we construct analytical expressions of four-parameters solutions; when all these parameters are equal to 0, we recover the Peregrine breather of order 3. It makes possible with this four-parameters representation, to generate all the types of patterns for the solutions, like the tria…
A Singular Multi-Grid Iteration Method for Bifurcation Problems
1984
We propose an efficient technique for the numerical computation of bifurcating branches of solutions of large sparse systems of nonlinear, parameter-dependent equations. The algorithm consists of a nested iteration procedure employing a multi-grid method for singular problems. The basic iteration scheme is related to the Lyapounov-Schmidt method and is widely used for proving the existence of bifurcating solutions. We present numerical examples which confirm the efficiency of the algorithm.
Concatenated trial based Hilbert-Huang transformation on event-related potentials
2010
Time-frequency analysis is critical to study event-related potentials (ERPs) now. ERPs are usually generated through averaging over a number of trials, and such averaging limits the application of a nonlinear time-frequency analysis method—Hilbert-Huang transformation (HHT). This is because HHT usually requires very long recordings to sufficiently decompose the complicated signal into oscillations and the averaged ERP trace tends to possess only hundreds of samples. Thus, this study designs the concatenated trial based HHT to release the limitation on the decomposition. Such a paradigm may reveal better temporal and spectral properties of an ERP than the conventional wavelet transformation …
A taxonomy for wavelet neural networks applied to nonlinear modelling
2008
This article presents a novel classification of wavelet neural networks based on the orthogonality/non-orthogonality of neurons and the type of nonlinearity employed. On the basis of this classification different network types are studied and their characteristics illustrated by means of simple one-dimensional nonlinear examples. For multidimensional problems, which are affected by the curse of dimensionality, the idea of spherical wavelet functions is considered. The behaviour of these networks is also studied for modelling of a low-dimension map.
Edge detection insensitive to changes of illumination in the image
2010
In this paper we present new edge detection algorithms which are motivated by recent developments on edge-adapted reconstruction techniques [F. Arandiga, A. Cohen, R. Donat, N. Dyn, B. Matei, Approximation of piecewise smooth functions and images by edge-adapted (ENO-EA) nonlinear multiresolution techniques, Appl. Comput. Harmon. Anal. 24 (2) (2008) 225-250]. They are based on comparing local quantities rather than on filtering and thresholding. This comparison process is invariant under certain transformations that model light changes in the image, hence we obtain edge detection algorithms which are insensitive to changes in illumination.
Intracrystalline Diffusion of Benzene in Ga-Silicate
1991
Abstract The sorption kinetics of benzene in large Ga-MFI crystals was investigated under constant volume- variable pressure conditions. A complete analysis of the uptake curves has been performed using solution of a nonlinear Volterra equation which describes the interaction of uptake process with the apparatus. Within the time scale of uptake measurements (10 3 -10 4 s) the uptake curves were found to be consistent with the solution of the second Fick's law. Corrected diffusion coefficients were found to be essentially independent of loading within the loading range investigated and in contrast to the system benzene-HNaZSM-5 [1,2] their temperature dependence is much stronger.
Eigenvalue Accumulation for Singular Sturm–Liouville Problems Nonlinear in the Spectral Parameter
1999
Abstract For certain singular Sturm–Liouville equations whose coefficients depend continuously on the spectral parameter λ in an interval Λ it is shown that accumulation/nonaccumulation of eigenvalues at an endpoint ν of Λ is essentially determined by oscillatory properties of the equation at the boundary λ = ν . As applications new results are obtained for the radial Dirac operator and the Klein–Gordon equation. Three other physical applications are also considered.
Non-Lipschitz Homogeneous Volterra Integral Equations
2018
In this chapter we introduce a class of nonlinear Volterra integral equations (VIEs) which have certain properties that deviate from the standard results in the field of integral equations. Such equations arise from various problems in shock wave propagation with nonlinear flux conditions. The basic equation we will consider is the nonlinear homogeneous Hammerstein–Volterra integral equation of convolution type $$\displaystyle u(t) = \int _0^t k(t-s) g(u(s))\,\mathrm {d}s. $$ When g(0) = 0, this equation has function u ≡ 0 as a solution (trivial solution). It is interesting to determine whether there exists a nontrivial solution or not. Classical results on integral equations are not to be …
H<inf>&#x221E;</inf> control of markovian switching systems with time-delays: Applied to DC-DC converters
2011
The DC-DC switching power converters are highly nonlinear systems. Consequently, the conventional linear controls based on averaging and linearization techniques will result in poor dynamic performance or system instability. In order to resolve this problem, in this paper a robust state feedback H∞ control is proposed for these systems under Markovian switching with mixed discrete, neutral and distributed delays. Based on the Lyapunov-Krasovskii functional theory, some required sufficient conditions are established in terms of delay-dependent linear matrix inequalities for the stochastic stability and stabilization of the considered system using some free matrices. The desired control is de…