We study a problem of energy exchange in a system of two coupled oscillators subject to 1 : 1 resonance. Our results exploit the concept of limiting phase trajectories LPTs . The LPT, associated with full energy transfer, is, in certain sense, an alternative to nonlinear normal modes characterized by conservation of energy. We consider two benchmark examples. As a first example, we construct an...

In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed states, namely amplitude death and oscillation death. The stabilization of saddle equilibrium point refers to the amplitude death state where oscillations are c...

In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the Duffing, Bonhoeffer-van der Pol and MLC circuit oscillators, we briefly explain the various bifurcations and chaos phenomena associated with these systems. We use n...

We report the experimental discovery of a remarkable organization of the set of self-generated periodic oscillations in the parameter space of a nonlinear electronic circuit. When control parameters are suitably tuned, the wave pattern complexity of the periodic oscillations is found to increase orderly without bound. Such complex patterns emerge forming self-similar discontinuous phases that c...

This paper proposes an on-off coupling process for chaos synchronization and information processing. An in depth analysis for the net effect of a conventional coupling is performed. The stability of the process is studied. We show that the proposed controlled coupling process can locally minimize the smoothness and the fidelity of dynamical data. A digital filter expression for the on-off coupl...

0960-0779/$ see front matter 2011 Elsevier Ltd doi:10.1016/j.chaos.2011.08.002 ⇑ Corresponding author. Tel.: +55 (11) 3091 6842 6706. E-mail address: [email protected] (E.S. Medeiros). In the bi-dimensional parameter space of driven oscillators, shrimp-shaped periodic windows are immersed in chaotic regions. For two of these oscillators, namely, Duffing and Josephson junction, we show that a weak h...

This paper investigates the resonant behaviour of silicon-based micro-oscillators with a length 3600 µm, width 1800 µm and thickness 10 over wide range ambient gas (N2) pressures, extending six orders magnitude from 10−3 mbar to 900 mbar. The oscillators are actuated piezoelectrically by thin-film aluminium-nitride (AlN) layer, cantilever coverage area being varied 33% up 100%. central focus is...

Duffing systems excited by harmonic excitations and subjected to noise additions are considered, it is examined whether the addition can be used steer response from one stable mode another. To help with this examination, authors propose a methodology for estimating probability that short duration Gaussian white generate or destroy modes of single nonlinear oscillator as well set coupled oscilla...