Search results for "nonlinear"
showing 10 items of 3684 documents
Solution of a cauchy problem for an infinite chain of linear differential equations
2005
Defining the recurrence relations for orthogonal polynomials we have found an exact solution of a Cauchy problem for an infinite chain of linear differential equations with constant coefficients. These solutions have been found both for homogeneous and an inhomogeneous systems.
The cauchy problem for non-linear Klein-Gordon equations
1993
We consider in ℝ n+1,n≧2, the non-linear Klein-Gordon equation. We prove for such an equation that there is a neighbourhood of zero in a Hilbert space of initial conditions for which the Cauchy problem has global solutions and on which there is asymptotic completeness. The inverse of the wave operator linearizes the non-linear equation. If, moreover, the equation is manifestly Poincare covariant then the non-linear representation of the Poincare Lie algebra, associated with the non-linear Klein-Gordon equation is integrated to a non-linear representation of the Poincare group on an invariant neighbourhood of zero in the Hilbert space. This representation is linearized by the inverse of the …
Existence and Regularity for a Class of Nonlinear Hyperbolic Boundary Value Problems
2002
AbstractThe regularity of the solution of the telegraph system with nonlinear monotone boundary conditions is investigated by two methods. The first one is based on D'Alembert-type representation formulae for the solution. In the second method the telegraph system is reduced to a linear Cauchy problem with a locally Lipschitzian functional perturbation; then regularity results are established by appealing to the theory of linear semigroups.
A shallow water model with eddy viscosity for basins with varying bottom topography
2001
The motion of an incompressible fluid confined to a shallow basin with a varying bottom topography is considered. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model to derive a two-dimensional shallow water model. The global regularity of the resulting model is proved. The anisotropic form of the stress tensor in our three-dimensional eddy viscosity model plays a critical role in ensuring that the resulting shallow water model dissipates energy.
Linear and nonlinear parametric model identification to assess granger causality in short-term cardiovascular interactions
2008
We assessed directional relationships between short RR interval and systolic arterial pressure (SAP) variability series according to the concept of Granger causality. Causality was quantified as the predictability improvement (PI) of a time series obtained when samples of the other series were used for prediction, i.e. moving from autoregressive (AR) to AR exogenous (ARX) prediction. AR and ARX predictions were performed both by linear and nonlinear parametric models. The PIs of RR given SAP and of SAP given RR, measuring baroreflex and mechanical couplings, were calculated in 15 healthy subjects in the resting supine and upright tilt positions. Using nonlinear models we found a bilateral i…
Modeling Local Social Migrations: A Cellular Automata Approach
2015
In local social migrations, agents move from their initial location looking for a better local social environment. Social migrations processes do not change the number of social agents of a given type (i.e., the empirical distribution of the population) but their spatial location. Although cellular automata seems to appear as a natural approach to model of social migrations, the evolution of the configuration through a cellular automata might induce a new configuration wherein the number of agents of each type might be actually modified. This article provides a characterization of these cellular automata rules such that for any initial empirical distribution, the evolution of the configurat…
Analysis of neuronal networks in the visual system of the cat using statistical signals--simple and complex cells. Part II.
1978
Superimposing additively a two-dimensional noise process to deterministic input signals (bars) the neurons of area 17 show a class-specific reaction for the task of signal extraction. Moving both parts of the signals simultaneously and varying the signal to noise ratio (S/N) the simple cells achieve the same performance as resulted from the psychophysical experiment. Type I complex cells extract moving deterministic signals (i.e. bars) from the stationary noise, whereas in the answers of Type II complex cells the statistical parts of the signals predominate. Considering the different cell types each as a series of a linear and a nonlinear system one obtains the cell specific space-time freq…
System-theoretical analysis of the Clare Bishop Area in the cat
1980
The Clare Bishop Area (CBA) is a retinotopically organized cortical area in the cat brain connected to a great variety of visual areas in a very complex wax (Fig. 1). Experimental analysis is difficult because of the following aspects: 1. As the distance from the retina increases, the signal combinations necessary to analyse the system become more and more specific. 2. Feedback loops cannot be opened, so an unequivocal identification of CBA cell properties is impossible. 3. The nonlinear character seems to have a great influence on signal processing. To circumvent these problems, specific signal combinations leading to a separation of input subsystems have been developed (Hoffmann and v. Se…
Stability analysis of neutral systems with mixed time-varying delays and nonlinear perturbations
2009
In this paper, the problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear perturbations are addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free weighting matrices and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range-dependent and distributed-delay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs) and can be easily solved by existing convex optimizat…
Nonlinear pattern recognition correlators based on color-encoding single-channel systems.
2004
In color pattern recognition, color channels are normally processed separately and afterward the correlation outputs are combined. This is the definition of multichannel processing. We combine a single-channel method with nonlinear filtering based on nonlinear correlations. These nonlinear correlations yield better discrimination than common matched filtering. The method codes color information as amplitude and phase distributions and is followed by correlations related to binary decompositions. The technique is based on binary decompositions of the red, green, and blue and the hue, saturation, and intensity monochromatic channels of the reference and of the input scene, after which the bin…