STIR: Multistability and Chaos in a Driven Nanowire System

Abstract

During the nine-month period of this STIR project, three things were done: (1) we discovered anti-phase synchronization in microelectromechanical (MEM) systems, (2) we uncovered a number of complex dynamical phenomena in nanoelectromechanical (NEM) systems, and (3) we developed an efficient, completely data-based method to detect unstable periodic orbits (UPOs) in high-dimensional chaotic systems. For (1), we showed that anti-phase synchronization can emerge in a pair of electrically coupled micro-mechanical beams. Under impulsive perturbation, desynchronization occurs, distorting the output of each beam. We derived a formula for the relaxation rate and verified it numerically. We also found that the difference between the displacements of the two beams, or the differential signal, is robustly immune to impulsive perturbation, implying that the system can effectively counter external disturbances. This can have significant applications in developing various micro-scale devices, which we elaborated using MEM resonators. For (2), we addressed the fundamental question of whether multistability can arise in high-dimensional physical systems. Motivated by the ever increasing widespread use of nanoscale systems, we investigated a prototypical class of NEM systems: electrostatically driven Si-nanowires, mathematically described by a set of driven, nonlinear partial differential equations. We developed a computationally efficient algorithm to solve the equations, and found that multistability and complicated structures of basin of attraction are common types of dynamics, and the latter can be attributed to extensive transient chaos. We also explored implications of these phenomena to device operations. For (3), we developed a framework, integrating the approximation theory of neural networks and adaptive synchronization, to address the problem of time-series based detection of UPOs in high-dimensional chaotic systems, and demonstrated the methodology using time series from the classic Mackey-Glass equation. The significance lies in the fact that detecting UPOs in chaotic systems based solely on time series has been a fundamental but extremely challenging problem in nonlinear dynamics, and previous approaches were applicable but mostly or low-dimensional chaotic systems. (a) Papers published in peer-reviewed journals (N/A for none) Enter List of papers submitted or published that acknowledge ARO support from the start of the project to the date of this printing. List the papers, including journal references, in the following categories:

Cite this paper

@inproceedings{Lai2013STIRMA, title={STIR: Multistability and Chaos in a Driven Nanowire System}, author={Ying-Cheng Lai}, year={2013} }