Optical spectral analysis of the nonlinear dynamics in long-wavelength single-mode VCSELs subject to orthogonal optical injection

2012 ◽  
Author(s):  
A. Quirce ◽  
P. Pérez ◽  
A. Valle ◽  
L. Pesquera
Keyword(s):  
Nonlinear Dynamics ◽  
Spectral Analysis ◽  
Single Mode ◽  
Optical Injection ◽  
Long Wavelength

Nonlinear Dynamics of an Imperfect Microbeam Under an Axial Load and Electric Excitation

2011 ◽  
Author(s):  
Laura Ruzziconi ◽  
Mohammad I. Younis ◽  
Stefano Lenci
Keyword(s):  
Nonlinear Dynamics ◽  
Microelectromechanical Systems ◽  
Complex Dynamics ◽  
Nonlinear Behavior ◽  
Single Mode ◽  
Phase Portraits ◽  
Nonlinear Phenomena ◽  
Theoretical Point ◽  
Initial Shape ◽  
Electric Excitation

This study is motivated by the growing attention, both from a practical and a theoretical point of view, toward the nonlinear behavior of microelectromechanical systems (MEMS). We analyze the nonlinear dynamics of an imperfect microbeam under an axial force and electric excitation. The imperfection of the microbeam, typically due to microfabrication processes, is simulated assuming the microbeam to be of a shallow arched initial shape. The device has a bistable static behavior. The aim is that of illustrating the nonlinear phenomena, which arise due to the coupling of mechanical and electrical nonlinearities, and discussing their usefulness for the engineering design of the microstructure. We derive a single-mode-reduced-order model by combining the classical Galerkin technique and the Pade´ approximation. Despite its apparent simplicity, this model is able to capture the main features of the complex dynamics of the device. Extensive numerical simulations are performed using frequency response diagrams, attractor-basins phase portraits, and frequency-dynamic voltage behavior charts. We investigate the overall scenario, up to the inevitable escape, obtaining the theoretical boundaries of appearance and disappearance of the main attractors. The main features of the nonlinear dynamics are discussed, stressing their existence and their practical relevance. We focus on the coexistence of robust attractors, which leads to a considerable versatility of behavior. This is a very attractive feature in MEMS applications. The ranges of coexistence are analyzed in detail, remarkably at high values of the dynamic excitation, where the penetration of the escape (dynamic pull-in) inside the double well may prevent the safe jump between the attractors.

scholarly journals CYCLIC DYNAMICS OF INFLATION: EMPIRICAL ANALYSIS

2017 ◽  
Vol 5 ◽  
pp. 396-400
Author(s):  
Alexander Protasov ◽  
Tatyana Kotcofana ◽  
Polina Stazhkova
Keyword(s):  
Nonlinear Dynamics ◽  
Twentieth Century ◽  
Spectral Analysis ◽  
Empirical Analysis ◽  
Price Levels ◽  
The World ◽  
Cyclic Dynamics ◽  
Dynamic Series

The paper is dedicated to the study of nonlinear dynamics of inflation. We hypothesize that in the second half of the twentieth century, inflation cycles replaced the pre-existing inflation-deflation cycles. This hypothesis is based on the study of data about price levels in various countries of the world for the period of 1950 to 2016. The paper shows some results of a spectral analysis that was applied to the dynamic series of prices. The results of the spectral analysis confirmed the hypothesis about the existence of inflation cycles.

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