Search results for "Linear system"
showing 10 items of 1558 documents
Path integral method for first-passage probability determination of nonlinear systems under levy white noise
2015
In this paper the problem of the first-passage probabilities determination of nonlinear systems under alpha-stable Lévy white noises is addressed. Based on the properties of alpha-stable random variables and processes, the Path Integral method is extended to deal with nonlinear systems driven by Lévy white noises with a generic value of the stability index alpha. Furthermore, the determination of reliability functions and first-passage time probability density functions is handled step-by-step through a modification of the Path Integral technique. Comparison with pertinent Monte Carlo simulation reveals the excellent accuracy of the proposed method.
Assessing nonlinear structures in real exchange rates using recurrence plot strategies
2002
Purchasing power parity (PPP) is an important theory at the basis of a large number of economic models. However, the implication derived from the theory that real exchange rates must follow stationary processes is not conclusively supported by empirical studies. In a recent paper, Serletis and Gogas [Appl. Finance Econ. 10 (2000) 615] show evidence of deterministic chaos in several OECD exchange rates. As a consequence, PPP rejections could be spurious. In this work, we follow a two-stage testing procedure to test for nonlinearities and chaos in real exchange rates, using a new set of techniques designed by Webber and Zbilut [J. Appl. Physiol. 76 (1994) 965], called recurrence quantificatio…
Two Nontrivial Solutions for Robin Problems Driven by a p–Laplacian Operator
2020
By variational methods and critical point theorems, we show the existence of two nontrivial solutions for a nonlinear elliptic problem under Robin condition and when the nonlinearty satisfies the usual Ambrosetti-Rabinowitz condition.
Basic Concepts and the Discovery of Solitons
1996
Today, many scientists see nonlinear science as the most deeply important frontier for the fundamental understanding of Nature. The soliton concept was firmly established after a gestation period of about one hundred and fifty years. Since then, different kinds of solitons have been observed experimentally in various real systems, and today, they have captured the imagination of scientists in most physical discipline. They are widely accepted as a structural basis for viewing and understanding the dynamic behavior of complex nonlinear systems. Before introducing the soliton concept via its remarkable and beautiful historical path we compare briefly the linear and nonlinear behavior of a sys…
Necessary and sufficient conditions for frequency entrainment of quasi-sinusoidal injection-synchonised oscillators
1986
A method is presented which permits the first-approximation exact analysis of the dynamical stability of fundamental-mode injectionsynchronized oscillators (FISO's) characterized by a quasi-sinusoidal quasi-static behavior. By combining small parameter and stroboscopic transformation techniques, the phase-lock stability investigation of an nth-order system is reduced to the simple Hurwitz test on an nth degree polynomial easily obtainable from steady state describing quantities. On this basis, equations for critical locking are also derived, which demonstrate the existence of a pair of limit curves (Locus and Boundary) already conjectured and looked for in the past, but only with partial su…
Integration of an LP Solver into Interval Constraint Propagation
2011
This paper describes the integration of an LP solver into iSAT, a Satisfiability Modulo Theories solver that can solve Boolean combinations of linear and nonlinear constraints. iSAT is a tight integration of the well-known DPLL algorithm and interval constraint propagation allowing it to reason about linear and nonlinear constraints. As interval arithmetic is known to be less efficient on solving linear programs, we will demonstrate how the integration of an LP solver can improve the overall solving performance of iSAT.
Identification of Nonlinear Systems Described by Hammerstein Models
2004
This paper deals with a method for identification of nonlinear systems suitable to be described by Hammerstein models consisting of a static nonlinearity followed by an ARX linear model. The estimation of the static nonlinearity is carried out supplying the system with a sequence of step signals of various amplitude and determining the corresponding steady-state responses. The estimation of the parameters of the ARX linear system is carried out by means of a least square estimator using data generated supplying the system with a Pseudorandom Binary Sequence (PRBS). The method in question is able to identify static nonlinearities of general type, also with hysteresis and/or discontinuities. …
Statistical analysis of multilayer perceptrons performances
2002
The paper is based on a series of studies on the learning capabilities of multilayered perceptrons (MLP). The complexity of these nonlinear systems can be varied, acting for instance on the number of hidden units, but we will be confronted with a choice dilemma, concerning the optimal complexity of the system for a given problem. By the mean of statistical methods, we have found that the effective number of hidden units is smaller than the potential size; some units have a "binary" activation level or a time constant activation. We also prove that weight initialization to small values is recommended and reduce the effective size of the hidden layer.
Indentation of rigidly supported sandwich beams with foam cores exhibiting non-linear compressive behaviour.
2011
A generalized analytical approach to investigate the indentation of sandwich beams under concentrated loads is presented, based on the Winkler foundation theory. A segment-wise model is implemented to the case of fully backed sandwich beams with polymeric foam cores exhibiting generic non-linear compressive behaviours. Closed-form analytical solutions of the indentation curve are obtained for simplified foam compression behaviours: elastic-perfectly-plastic, bilinear and bilinear-perfectly-plastic. Analytical predictions are compared with experimental data from sandwiches employing foam cores with peculiar non-linear behaviours. The proposed models are found to give a better match of the e…
Numerical solution of a class of nonlinear boundary value problems for analytic functions
1982
We analyse a numerical method for solving a nonlinear parameter-dependent boundary value problem for an analytic function on an annulus. The analytic function to be determined is expanded into its Laurent series. For the expansion coefficients we obtain an operator equation exhibiting bifurcation from a simple eigenvalue. We introduce a Galerkin approximation and analyse its convergence. A prominent problem falling into the class treated here is the computation of gravity waves of permanent type in a fluid. We present numerical examples for this case.