Search results for "Nonlinear system"
showing 10 items of 1446 documents
Application of a non linear local analysis method for the problem of mixed convection instability
2007
Abstract We consider the problem of laminar mixed convection flow between parallel, vertical and uniformly heated plates where the governing dimensionless parameters are the Prandtl, Rayleigh and Reynolds numbers. Using the method based on the centre manifold theorem which was derived from the general theory of dynamical systems, we reduce a three-dimensional simplified model of ordinary differential amplitude equations emanating from the original Navier-Stokes system of the problem in the vicinity of a trivial stationary solution. We have found that when the forcing parameter, the Rayleigh number, increases beyond the critical value Ra s , the stationary solution is a pitchfork bifurcation…
Behavior of gap solitons in anharmonic lattices
2017
International audience; Using the theory of bifurcation, we provide and find gap soliton dynamics in a nonlinear Klein-Gordon model with anharmonic, cubic, and quartic interactions immersed in a parametrized on-site substrate potential. The case of a deformable substrate potential allows theoretical adaptation of the model to various physical situations. Nonconvex interactions in lattice systems lead to a number of interesting phenomena that cannot be produced with linear coupling alone. By investigating the dynamical behavior and bifurcations of solutions of the planar dynamical systems, we derive a variety of exotic solutions corresponding to the phase trajectories under different paramet…
Time-dependent density-functional theory in the projector augmented-wave method
2008
We present the implementation of the time-dependent density-functional theory both in linear-response and in time-propagation formalisms using the projector augmented-wave method in real-space grids. The two technically very different methods are compared in the linear-response regime where we found perfect agreement in the calculated photoabsorption spectra. We discuss the strengths and weaknesses of the two methods as well as their convergence properties. We demonstrate different applications of the methods by calculating excitation energies and excited state Born–Oppenheimer potential surfaces for a set of atoms and molecules with the linear-response method and by calculating nonlinear e…
Nonlinear economic growth: Some theory and cross-country evidence
2007
Abstract This paper aims to test the existence of different growth regimes, that is of different relationships between growth rate and income level. We propose a simple nonlinear growth model and test its empirical implications by estimating Markov transition matrices and stochastic kernels. We show that growth is indeed nonlinear: a first phase of slow or zero growth is followed by a take-off and, finally, by a phase of deceleration. We discuss the relevance of these results with respect to the issue of convergence and reversibility of development, in the light of models of structural change and technological diffusion.
Nonlinearity in intergenerational income transmission: A cross-country analysis
2016
Abstract The aim of this paper is to explore nonlinearity in intergenerational income transmission. We use a set of occupational tables in different countries to test nonlinearity. We also empirically address how policy variables can affect nonlinearity. Our findings suggest that concavity is supported in those societies with less credit constraints, but with more poverty and income inequality; education has an increasing effect on convexity.
Threshold cointegration and nonlinear adjustment between stock prices and dividends
2008
According to several empirical studies, the linear present-value model fails to explain the behaviour of stock prices in the long run. We analyse the possible presence of threshold cointegration between real stock prices and dividends for the US market during the period from 1871:1 to 2004:6. According to our results, the null hypothesis of linear cointegration between stock prices and dividends is rejected in favour of a two-regime threshold cointegration model. We find also that stock prices do not respond to equilibrium error, and dividends respond to the past divergence only if the deviation from the equilibrium error does not exceed the estimated threshold parameter. This in turn would…
A note on nonlinear dynamics in the Spanish term structure of interest rates
2006
Abstract This note applies the methodology to test for threshold cointegration recently proposed by Hansen and Seo (2002) [Hansen, B. E. & Seo, B., (2002). Testing for two-regime threshold cointegration in vector error-correction models. Journal of Econometrics, 110, 293–318] to the Spanish term structure of interest rates during the period 1980:1–2002:12. The evidence suggests that nonlinear cointegration between long and short interest rates is clearly rejected, so that a linear cointegration model would provide an adequate empirical description for the Spanish term structure of interest rate.
The closed-form solution for a family of four-dimension nonlinear MHDS
2008
In this article we propose a method for solving a general class of four-dimension nonlinear modified Hamiltonian dynamic systems in closed form. This method may be used to study several intertemporal optimization problems sharing a common structure, which involves unbounded technological constraints as well as multiple controls and state variables. The method is developed by solving the first-order conditions associated with the planner's problem corresponding to the Lucas [1988. On the mechanics of economic development. Journal of Monetary Economics 22, 3-42] two-sector model of endogenous growth, and allows for explicitly showing the transitional dynamics of the model. Despite the externa…
Nonlinear GARCH models for highly persistent volatility
2005
In this paper we study new nonlinear GARCH models mainly designed for time series with highly persistent volatility. For such series, conventional GARCH models have often proved unsatisfactory because they tend to exaggerate volatility persistence and exhibit poor forecasting ability. Our main emphasis is on models that are similar to previously introduced smooth transition GARCH models except for the novel feature that a lagged value of conditional variance is used as the transition variable. This choice of the transition variable corresponds to the idea that high persistence in conditional variance is related to relatively infrequent changes in regime. U sing the theory of Markov chains w…
Nonlinear impact estimation in spatial autoregressive models
2018
International audience; This paper extends the literature on the calculation and interpretation of impacts for spatial autoregressive models. Using a Bayesian framework, we show how the individual direct and indirect impacts associated with an exogenous variable introduced in a nonlinear way in such models can be computed, theoretically and empirically. Rather than averaging the individual impacts, we suggest to graphically analyze them along with their confidence intervals calculated from Markov chain Monte Carlo (MCMC). We also explicitly derive the form of the gap between individual impacts in the spatial autoregressive model and the corresponding model without a spatial lag and show, in…