Search results for "nonlinear system"
showing 10 items of 1446 documents
Oscillation of second-order nonlinear differential equations with damping
2014
Abstract We study oscillatory properties of solutions to a class of nonlinear second-order differential equations with a nonlinear damping. New oscillation criteria extend those reported in [ROGOVCHENKO, Yu. V.—TUNCAY, F.: Oscillation criteria for second-order nonlinear differential equations with damping, Nonlinear Anal. 69 (2008), 208–221] and improve a number of related results.
Infinitely many solutions for a perturbed nonlinear Navier boundary value problem involving the -biharmonic
2012
By using critical point theory, we establish the existence of infinitely many weak solutions for a class of elliptic Navier boundary value problems depending on two parameters and involving the p-biharmonic operator. © 2012 Elsevier Ltd. All rights reserved.
Kleine periodische L�sungen bei nichtlinearen stark-elliptischen Systemen von partiellen Differentialgleichungen I
1971
Strongly elliptic systems of nonlinear partial differential equations are considered in the case when the derivatives of the solutions occuring in the nonlinear terms have the same order as those in the linear principal part. The existence of periodic solutions for such systems is investigated. It is shown that this problem can be reduced to the study of algebraic bifurcation equations, whose small solutions correspond to the classical solutions of the given problem. A discussion of the bifurcation equations will be given in a forthcoming paper.
Laplace’s Method of Integration in the Path Integral Approach for the Probabilistic Response of Nonlinear Systems
2020
In this paper the response of nonlinear systems under stationary Gaussian white noise excitation is studied. The Path Integral (PI) approach, generally employed for evaluating the response Probability Density Function (PDF) of systems in short time steps based on the Chapman-Kolmogorov equation, is here used in conjunction with the Laplace’s method of integration. This yields an approximate analytical solution of the integral involved in the Chapman-Kolmogorov equation. Further, in this manner the repetitive integrations, generally required in the conventional numerical implementation of the procedure, can be circumvented. Application to a nonlinear system is considered, and pertinent compa…
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.