A general energy-based theory of autoresonance (self-sustained resonance) in low-dimensional nonautonomous systems is presented. The equations that together govern the autoresonance solutions and excitations are derived with the aid of a variational principle concerning the power functional. These equations provide a feedback autoresonance-controlling mechanism. The theory is applied to Duffing...

In this paper, an improved technique for constructing Chaotic Shift Keying (CSK) for transmitting digital signals is introduced. In contrast to the classical methods where only two chaotic attractors, representing logic 0 and logic 1 are used to build CSK, the proposed system allows the chaotic transmitted signal to alternate among four different chaotic attractors. In addition, the transmitter...

ACILINA CANECO Instituto Superior de Engenharia de Lisboa, Mathematics Unit, DEETC and CIMA-UE, Rua Conselheiro Emidio Navarro, 1, 1949-014 Lisboa, Portugal E-mail: [email protected] J. LEONEL ROCHA Instituto Superior de Engenharia de Lisboa, Mathematics Unit, DEQ, and CEAUL, Rua Conselheiro Emidio Navarro, 1, 1949-014 Lisboa, Portugal E-mail: [email protected] CLARA GRÁCIO Departm...

By taking two-coupled duffing oscillator system as the research object, the study found under the synergistic effect of weak periodic signal and noise, the two-coupled duffing oscillator system has typical stochastic resonance and even could achieve better output of stochastic resonance than single duffing oscillator. Based on this phenomenon, this paper proposes a new method to detect the weak...

We study the manner in which the effect of quasiperiodic modulation is transmitted in a coupled nonlinear dynamical system. A system of Rössler oscillators is considered, one of which is subject to driving, and the dynamics of other oscillators which are, in effect, indirectly forced is observed. Strange nonchaotic dynamics is known to arise only in quasiperiodically driven systems, and thus th...

The cutting sound in the audible range includes plenty of tool wear information. The sound is sampled by the acoustic emission AE sensor as a short-time sequence, then worn wear can be detected by the Duffing-Holmes oscillator. A novel engineering method is proposed for determining the chaotic threshold of the Duffing-Holmes oscillator. First, a rough threshold value is calculated by local Lyap...

In this paper we have chosen to work with two different approaches solving the inverse problem of calculus variation. The first approach is based on an integral representation Lagrangian function that uses equation motion while second one relies a generalization well known Noether's theorem and constructs directly from motion. As application provide some useful remarks for modified Emden-type t...

Parametrically excited oscillators are used in several domains, particular to improve the dynamical behaviour of systems like case parametric amplification or energy harvesting. Although dry friction is often omitted during system modelling due complexity its nonsmooth nature, it sometimes necessary account for this kind damping adequately represent motion. In paper, proposed investigate effect...

‎A numerical technique based on the collocation method using Legendre multiwavelets are‎ ‎presented for the solution of forced Duffing equation‎. ‎The operational matrix of integration for ‎Legendre multiwavelets is presented and is utilized to reduce the solution of Duffing equation‎ ‎to the solution of linear algebraic equations‎. ‎Illustrative examples are included to demonstrate‎ ‎the valid...

In this article, we consider the nonlinear Duffing-van der Pol-type oscillator system by means of the first integral method. This system has physical relevance as a model in certain flow-induced structural vibration problems, which includes the van der Pol oscillator and the damped Duffing oscillator etc as particular cases. Firstly, we apply the Division Theorem for two variables in the comple...