we are concerned with perturbations of the Hamiltonian system of the type c L(t)q + W&, q) = 0, t E R, WI where q = (ql, , qN) E WN, W E C1(W x WN,R), and L(t) E C(W,WN2) is a positive definite symmetric matrix. Variational arguments are used to prove the existence of homoclinic solutions for system (HS). @ 2003 Elsevier Science Ltd. All rights reserved. KeywordsHomoclinic orbits, Duffing equat...

This paper deals with the design of feedback controllers for a chaotic dynamical system l i e the Duffing equation. Lyapunov theory is used to show that the proposed bounded controllers achieve global convergence for any desired trajectory. Some simulation examples illustrate the presented ideas.

Some recent developments for the validation of nonlinear models built from data are reviewed. Besides giving an overall view of the field, a procedure is proposed and investigated based on the concept of dissipative synchronization between the data and the model, which is very useful in validating models that should reproduce dominant dynamical features, like bifurcations, of the original syste...

A new class of time-integrators is presented for strongly nonlinear dynamical systems. These algorithms are far superior to the currently common time integrators in computational efficiency and accuracy. These three algorithms are based on a local variational iteration method applied over a finite interval of time. By using Chebyshev polynomials as trial functions andDirac–Delta functions as th...

The paper deals with the problem of estimation of the topological entropy for non-autonomous systems of differential equations via the second (direct) Lyapunov method. The main result of the paper is illustrated by examples concerning the Lorenz system and Duffing oscillator.

In this paper, we investigate the existence and uniqueness of almost periodic solutions for a class of nonlinear Duffing system with time-varying delays. By using theory of exponential dichotomies and contraction mapping principle, we establish some new results and give an example to illustrate the theoretical analysis in this work.

In this work, traveling wave solutions of (1+1)-dimensional Landau-Ginzburg-Higgs and Duffing nonlinear partial differential equations, which are examples mathematical modeling, obtained analyzed using the modified exponential function method. order to facilitate physical interpretation models represented by these simulations behavior model as three-dimensional, contour, density two-dimensional...