相关论文: The parameterization method for center manifolds

A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…

Parametric prediction error methods constitute a classical approach to the identification of linear dynamic systems with excellent large-sample properties. A more recent regularized approach, inspired by machine learning and Bayesian…

In this paper, we give a direct method to study the isochronous centers on center manifolds of three dimensional polynomial differential systems. Firstly, the isochronous constants of the three dimensional system are defined and its…

The method of keplerization of one-body motion in any central force field, introduced by Martinusi and Gurfil in 2012, is reviewed and reformulated into a general homogenization method which applies to any kind of bounded motion. It is also…

We rigorously show that a class of systems of partial differential equations modeling wave bifurcations supports stationary equivariant bifurcation dynamics through deriving its full dynamics on the center manifold(s). A direct consequence…

In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…

The nonlinear systems obtained by discretizing degenerate parabolic equations may be hard to solve, especially with Newton's method. In this paper, we apply to Richards equation a strategy that consists in defining a new primary unknown for…

A parameter estimation method is devised for a slow-fast stochastic dynamical system, where often only the slow component is observable. By using the observations only on the slow component, the system parameters are estimated by working on…

Conjugate line parametrizations of surfaces were first discretized almost a century ago as quad meshes with planar faces. With the recent development of discrete differential geometry, two discretizations of principal curvature line…

In this report we consider the parameterization of low-dimensional manifolds that are specified (approximately) by a set of points very close to the manifold in the original high-dimensional space. Our objective is to obtain a…

Transformation-invariant analysis of signals often requires the computation of the distance from a test pattern to a transformation manifold. In particular, the estimation of the distances between a transformed query signal and several…

In this paper, we investigate properties of entropy-penalized Wasserstein barycenters introduced by Bigot, Cazelles and Papadakis (2019) as a regularization of Wasserstein barycenters first presented by Agueh and Carlier (2011). After…

I prove that a centre manifold approach to creating finite difference models will consistently model linear dynamics as the grid spacing becomes small. Using such tools of dynamical systems theory gives new assurances about the quality of…

This article is devoted to the application of the parametrisation method for invariant manifold with a complex normal form style (CNF), for the derivation of high-order approximations of underdamped nonlinear dispersion relationships for…

We develop a stochastic parametrization, based on a `simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike…

A general input-output modelling technique for aperiodic-sampling linear systems has been developed. The procedure describes the dynamics of the system and includes the sequence of sampling periods among the variables to be handled. Some…

Using the methods from topological dynamics, H. Furstenberg introduced the notions of Central sets and proved the famous Central Sets Theorem which is the simultaneous extension of the van der Waerden and Hindman Theorem. Later N. Hindman…

In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply…

The Bayesian formulation of inverse problems is attractive for three primary reasons: it provides a clear modelling framework; means for uncertainty quantification; and it allows for principled learning of hyperparameters. The posterior…

This paper bridges synthetic and classical differential geometry by investigating the metrizability and dynamics of Weil bundles. For a smooth, compact manifold \(M\) and a Weil algebra \(\mathbf{A}\), we prove that the manifold…