In a previous paper (Comput. Methods Appl. Mech. Engrg 170, 223-237, 1999) we introduced a new method for computing the dominant Lyapunov exponent of a chaotic map by using spatial integration involving a matrix norm. We conjectured that this sequence of integrals decayed proportional to 1/n. We now prove this conjecture and derive a bound on the next term in the asymptotic expansion of the ter...

We explore the transition to in-phase synchronization in globally coupled oscillator arrays, and compare results for van der Pol arrays with Josephson junction arrays. Our approach yields in each case an analytically tractable iterative map; the resulting stability formulas are simple because the expansion procedure identifies natural parameter groups. A third example, an array of Duffing-van d...

In the last decade we have witnessed exciting technological advances in the fabrication and control of microelectromechanical and nanoelectromechanical systems (MEMS&NEMS) [16, 19, 26, 54, 55]. Such systems are being developed for a host of nanotechnological applications, such as highly sensitive mass [25, 34, 67], spin [56], and charge detectors [17, 18], as well as for basic research in the m...

Phase-control techniques of chaos aim to extract periodic behaviors from chaotic systems by applying weak harmonic perturbations with a suitably chosen phase. However, little is known about the best strategy for selecting adequate perturbations to reach desired states. Here we use experimental measures and numerical simulations to assess the benefits of controlling individually the three terms ...

We investigate the dynamic quantum tunneling between two attractors of a mesoscopic driven Duffing oscillator. We find that, in addition to inducing a remarkable quantum shift of the bifurcation point, the mesoscopic nature also results in a perfect linear scaling behavior for the tunneling rate with the driving distance to the shifted bifurcation point.

Synchronization in the system of coupled non-identical nonisochronous Van fer Pol – Duffing oscillators with inertial and dissipative coupling is discussed. Generalized Adler’s equation is obtained and investigated in the presence of all relevant factors affecting the synchronization (nonisochronism of the oscillators, their nonidentity, coupling of the dissipative and inertial type). Character...

An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the generalized harmonic balance method in which analytical approximate solutions have a rational form. This approach gives us not only a truly periodic solution but also the frequency of motion as a function of the amplitude of oscillation. Three truly nonlinear oscillators ...

<p style='text-indent:20px;'>The present document outlines a non-linear control theory, based on the PID regulation scheme, to synchronize two second-order dynamical systems insisting Riemannian manifold. The devised extended referred as M-PID, includes an unconventional component, termed 'canceling component', whose purpose is cancel natural dynamics of system and replace it with desired...