Search results for "Linear system"

<title>Reaction-diffusion electrical network for image processing</title>

2006

We consider an experimental setup, modelling the FitzHugh-Nagumo equation without recovery term and composed of a 1D nonlinear electrical network made up of discrete bistable cells, resistively coupled. In the first place, we study the propagation of topological fronts in the continuum limit, then in more discrete case. We propose to apply these results to the domain of signal processing. We show that erosion and dilation of a binary signal, can be obtained. Finally, we extend the study to 2D lattices and show that it can be of great interest in image processing techniques.© (2006) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted fo…

Solvability of nonlinear equations in spectral gaps of the linearization

1992

Keywords: strongle indefinite ; nonlinear Hill's equation Reference ANA-ARTICLE-1992-002doi:10.1016/0362-546X(92)90116-VView record in Web of Science Record created on 2008-12-10, modified on 2016-08-08

Existence and uniqueness of solutions to a quasilinear parabolic equation with quadratic gradients in financial markets

2005

A quasilinear parabolic equation with quadratic gradient terms is analyzed. The equation models an optimal portfolio in so-called incomplete financial markets consisting of risky assets and non-tradable state variables. Its solution allows to compute an optimal portfolio strategy. The quadratic gradient terms are essentially connected to the assumption that the so-called relative risk aversion function is not logarithmic. The existence of weak global-in-time solutions in any dimension is shown under natural hypotheses. The proof is based on the monotonicity method of Frehse. Furthermore, the uniqueness of solutions is shown under a smallness condition on the derivatives of the covariance (?…

Noise Enhanced Stability in Fluctuating Metastable States

2004

We derive general equations for the nonlinear relaxation time of Brownian diffusion in randomly switching potential with a sink. For piece-wise linear dichotomously fluctuating potential with metastable state, we obtain the exact average lifetime as a function of the potential parameters and the noise intensity. Our result is valid for arbitrary white noise intensity and for arbitrary fluctuation rate of the potential. We find noise enhanced stability phenomenon in the system investigated: the average lifetime of the metastable state is greater than the time obtained in the absence of additive white noise. We obtain the parameter region of the fluctuating potential where the effect can be o…

Instability and bistability during the growth of a corrosion scale on metals and alloys

1986

This paper summarizes the main results for the interpretation of the self organized corrosion scales observed in oxidation or sulfidation of some metals or alloys. It consists also of a reconsideration of the classical theoretical concepts used in Reactivity of Solids. It proposes new theoretical tools that have been fruitfully utilized in other topics : non linear and coupled processes, stability analysis and bifurcation theory. Some examples are developed, where the corrosion kinetics at high temperature are interpreted in term of chemical bistable system able to oscillate spontaneously and mechanochemical couplings are also taken into account. In according with experimental results, all …

Extended Entropy Functional for Nonlinear Systems in Stochastic Dynamics

2002

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 …