Analytical calculation of the transition to complete phase synchronization in coupled oscillators

Here we present a system of coupled phase oscillators with nearest neighbors coupling, which we study for different boundary conditions. We concentrate at the transition to the total synchronization. We are able to develop exact solutions for the value of the coupling parameter when the system becomes completely synchronized, for the case of periodic boundary conditions as well as for a chain with fixed ends. We compare the results with those calculated numerically.

Geometrical properties of coupled oscillators at synchronization

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Transition to complete synchronization in phase-coupled oscillators with nearest neighbor coupling

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Multistable behavior above synchronization in a locally coupled Kuramoto model

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Basins of attraction changes by amplitude constraining of oscillators with limited power supply

We investigate the dynamics of a Duffing oscillator driven by a limited power supply, such that the source of forcing is considered to be another oscillator, coupled to the first one. The resulting dynamics come from the interaction between both systems. Moreover, the Duffing oscillator is subjected to collisions with a rigid wall (amplitude constraint). Newtonian laws of impact are combined with the equations of motion of the two coupled oscillators. Their solutions in phase space display periodic (and chaotic) attractors, whose amplitudes, especially when they are too large, can be controlled by choosing the wall position in suitable ways. Moreover, their basins of attraction are significantly modified, with effects on the final state system sensitivity. (c) 2005 Elsevier Ltd. All rights reserved.

On an Active Control for a Structurally Nonlinear Mechanical System, Taking Into Account an Energy Pumping

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Some remarks on bifurcation analysis of a nonlinear vibrating system excited by a shape memory alloy material (SMA)

In this paper, the dynamical response of a coupled oscillator is investigated, taking in consideration the nonlinear behavior of a SMA spring coupling the two oscillators. Due to the nonlinear coupling terms, the system exhibits both regular and chaotic motions. The Poincaré sections for different sets of coupling parameters are verified. © 2011 World Scientific Publishing Company.

Application of passive control to energy harvester efficiency using a nonideal portal frame structural support system

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Determination of the critical coupling for oscillators in a ring

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Gap solitons in Bose-Einstein condensates in linear and nonlinear optical lattices

Properties of localized states on array of BEC confined to a potential, representing superposition of linear and nonlinear optical lattices are investigated. For a shallow lattice case the coupled mode system has been derived. We revealed new types of gap solitons and studied their stability. For the first time a moving soliton solution has been found. Analytical predictions are confirmed by numerical simulations of the Gross-Pitaevskii equation with jointly acting linear and nonlinear periodic potentials. (c) 2007 Elsevier B.V. All rights reserved.

Carbon monoxide oxidation over platinum: Stable, oscillatory and quasi-chaotic regimes

We model the heterogeneously catalyzed oxidation of CO over a Pt surface. A phase diagram analysis is used to probe the several steady state regimes and their stability. We incorporate an experimentally observed 'slow' sub-oxide kinetic step, thereby generalizing a previously presented model. In agreement with experimental data, stable, oscillatory and quasi-chaotic regimes are obtained. Furthermore, the inclusion of the sub-oxide step yields a relaxation oscillation regime. © 1998 Elsevier Science B.V. All rights reserved.

Técnica híbrida de plasma para a deposição de filmes de alumina

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the effects of system parameters on the response of a harmonically excited system consisting of weakly coupled nonlinear and linear oscillators

This paper discusses the dynamic behaviour of a nonlinear two degree-of-freedom system consisting of a harmonically excited linear oscillator weakly connected to a nonlinear attachment having linear and cubic restoring forces. The effects of the system parameters on the shape of the frequency-response curve are investigated, in particular those yielding the appearance and disappearance of outer and inner detached resonance curves. In contrast to the case when the linear stiffness of the attachment is zero, it is found that multivaluedness occurs at low frequencies as the resonant peak bends to the right. It is also found that as the coefficient of the linear term increases, the range of parameters yielding detached curves reduces. Compared to the case when the attached system has no linear stiffness term, this range of parameters corresponds to smaller values of the damping and nonlinear coefficients. Approximate analytical expressions for the jump-up and jump-down frequencies of the system under investigation are also derived. (C) 2011 Elsevier Ltd. All rights reserved.

Exact propagator beyond and at caustics for isotropic time-dependent coupled and driven oscillators

Through a sequence of transformations we relate the propagator for the system of isotropic time-dependent, coupled and driven oscillators with time-varying mass, with those of free particles. We then derive the wave functions and the propagator beyond and at caustics. Finally we study a particular case which appears in quantum optics. © 1990.

Dressed (renormalized) coordinates in a nonlinear system

In previous publications, the concepts of dressed coordinates and dressed states have been introduced in the context of a harmonic oscillator linearly coupled to an infinity set of other harmonic oscillators. In this paper, we show how to generalize such dressed coordinates and. states to a nonlinear version of the mentioned system. Also, we clarify some misunderstandings about the concept of dressed coordinates. Indeed, now we: prefer to call them renormalized coordinates to emphasize the analogy with the renormalized fields in quantum field theory.