SPATIOTEMPORAL STRUCTURES IN UNDOPED PHOTOEXCITED SEMICONDUCTOR SUPERLATTICES

2001 ◽  
Vol 11 (11) ◽  
pp. 2817-2822 ◽  
Author(s):  
A. PERALES ◽  
L. L. BONILLA ◽  
M. MOSCOSO ◽  
J. GALÁN
Keyword(s):  
Degrees Of Freedom ◽  
Dynamical Behavior ◽  
Nonlinear Dynamical System ◽  
Nonlinear Behavior ◽  
Numerical Continuation ◽  
Continuation Methods ◽  
Semiconductor Superlattices ◽  
Nonlinear Dynamical ◽  
Strongly Nonlinear ◽  
Parameter Ranges

Semiconductor superlattices are a very interesting example of a nonlinear dynamical system with a large number of degrees of freedom. They show a strongly nonlinear behavior and they are well suited for the observation of current instabilities. In the present work, the dynamical behavior of undoped photoexcited superlattices has been analyzed by numerical continuation methods and bifurcation theory within the framework of a simple drift-diffusion model. The control parameters are the applied dc voltage and the carrier density, which are related to the laser power. We compile our results in a phase diagram and locate the lines where the system undergoes qualitative changes of behavior. The oscillatory regions are related to the appearance and disappearance of Hopf tongue crossings, for which oscillations appear as sub- or supercritical bifurcations. This implies the existence of voltage windows of current oscillations and hysteresis in appropriate parameter ranges, which agrees with recent experimental observations.

Beating Effects in a Single Nonlinear Dynamical System in a Neighborhood of the Resonance

2016 ◽  
Vol 849 ◽  
pp. 76-83
Author(s):  
Jiří Náprstek ◽  
Cyril Fischer
Keyword(s):  
Harmonic Balance ◽  
Excitation Frequency ◽  
Nonlinear Dynamical System ◽  
Numerical Continuation ◽  
System Response ◽  
Algebraic Equations ◽  
Single Degree Of Freedom ◽  
Nonlinear Dynamical ◽  
The Difference ◽  
Eigen Frequency

The exact coincidence of external excitation and basic eigen-frequency of a single degree of freedom (SDOF) nonlinear system produces stationary response with constant amplitude and phase shift. When the excitation frequency differs from the system eigen-frequency, various types of quasi-periodic response occur having a character of a beating process. The period of beating changes from infinity in the resonance point until a couple of excitation periods outside the resonance area. Theabove mentioned phenomena have been identified in many papers including authors’ contributions. Nevertheless, investigation of internal structure of a quasi-period and its dependence on the difference of excitation and eigen-frequency is still missing. Combinations of harmonic balance and small parameter methods are used for qualitative analysis of the system in mono- and multi-harmonic versions. They lead to nonlinear differential and algebraic equations serving as a basis for qualitativeanalytic estimation or numerical description of characteristics of the quasi-periodic system response. Zero, first and second level perturbation techniques are used. Appearance, stability and neighborhood of limit cycles is evaluated. Numerical phases are based on simulation processes and numerical continuation tools. Parametric evaluation and illustrating examples are presented.

Stable and Unstable Quasiperiodic Oscillations in Robot Dynamics

1993 ◽  
Author(s):  
G. Stépán ◽  
G. Haller
Keyword(s):  
Nonlinear Dynamical Systems ◽  
Dynamical Behavior ◽  
Time Lag ◽  
Nonlinear Behavior ◽  
Degree Of Freedom ◽  
Robot Dynamics ◽  
Robot Arm ◽  
Delayed Systems ◽  
Nonlinear Dynamical ◽  
Quasiperiodic Oscillations

Abstract Delays in robot control may result in unexpectedly sophisticated nonlinear dynamical behavior. Experiments on force controlled robots frequently show periodic and quasiperiodic oscillations which cannot be explained without including the time lag and/or the sampling time of the system in our models. Delayed systems, even of low degree of freedom, can produce phenomena which are already well understood in the theory of nonlinear dynamical systems but hardly ever occur in simple mechanical models. To illustrate this, we analyze the delayed positioning of a single degree of freedom robot arm. The analytical results show typical nonlinear behavior in the system which may go through a codimension two Hopf bifurcation for an infinite set of parameter values, leading to the creation of two-tori in the phase space. These results give a qualitative explanation for the existence of self-excited quasiperiodic oscillations in the dynamics of force controlled robots.

A New Method for Equilibria and Stability Analysis of Nonlinear Dynamical Systems

2014 ◽  
Vol 534 ◽  
pp. 131-136
Author(s):  
Long Cao ◽  
Yi Hua Cao
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Numerical Continuation ◽  
Vehicle Model ◽  
Nonlinear Dynamical ◽  
Novel Method ◽  
Linearized System ◽  
Continuation Algorithm

A novel method based on numerical continuation algorithm for equilibria and stability analysis of nonlinear dynamical system is introduced and applied to an aircraft vehicle model. Dynamical systems are usually modeled with differential equations, while their equilibria and stability analysis are pure algebraic problems. The newly-proposed method in this paper provides a way to solve the equilibrium equation and the eigenvalues of the locally linearized system simultaneously, which avoids QR iterations and can save much time.

INFLUENCE OF ENVIRONMENTAL NOISE ON THE DYNAMICS OF A REALISTIC ECOLOGICAL MODEL

2007 ◽  
Vol 07 (01) ◽  
pp. L61-L77 ◽  
Author(s):  
R. K. UPADHYAY ◽  
A. MUKHOPADHYAY ◽  
S. R. K. IYENGAR
Keyword(s):  
Ecological Model ◽  
Dynamical Behavior ◽  
Nonlinear Dynamical System ◽  
Growth Parameter ◽  
Environmental Noise ◽  
Model System ◽  
Dynamical System Theory ◽  
Chain Model ◽  
Nonlinear Dynamical ◽  
Food Chain Model

The present paper investigates the influence of environmental noise on a fairly realistic three-species food chain model based on the Leslie-Gower scheme. The self- growth parameter for the prey species is assumed to be perturbed by white noise characterized by a Gaussian distribution with mean zero and unit spectral density. Using tools borrowed from the nonlinear dynamical system theory, we study the dynamical behavior of the model system. The behavior of the stochastic system (perturbed one) is studied and the fluctuations in the populations are measured both analytically (for the linearized system) and numerically by computer simulation. Varying one of the control parameters in its range, while keeping all the others constant, we monitor the changes in the dynamical behavior of the model system, thereby fixing the regimes in which the system exhibits chaotic dynamics. Our study suggests that the trophic level (top, middle or bottom) at which a population is positioned, the amplitude of environmental noise and the population's susceptibility to environmental noise play key roles in how noise affects the population dynamics.

scholarly journals Standing Swells Surveyed Showing Surprisingly Stable Solutions for the Lorenz '96 Model

2014 ◽  
Vol 24 (10) ◽  
pp. 1430027 ◽  
Author(s):  
Morgan R. Frank ◽  
Lewis Mitchell ◽  
Peter Sheridan Dodds ◽  
Christopher M. Danforth
Keyword(s):  
Parameter Space ◽  
Chaotic Dynamics ◽  
Degrees Of Freedom ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Standing Waves ◽  
Nonlinear Dynamical ◽  
Hidden Order ◽  
Stable Solutions ◽  
Lorenz 96

The Lorenz '96 model is an adjustable dimension system of ODEs exhibiting chaotic behavior representative of the dynamics observed in the Earth's atmosphere. In the present study, we characterize statistical properties of the chaotic dynamics while varying the degrees of freedom and the forcing. Tuning the dimensionality of the system, we find regions of parameter space with surprising stability in the form of standing waves traveling amongst the slow oscillators. The boundaries of these stable regions fluctuate regularly with the number of slow oscillators. These results demonstrate hidden order in the Lorenz '96 system, strengthening the evidence for its role as a hallmark representative of nonlinear dynamical behavior.

scholarly journals Minimal blowing pressure allowing periodic oscillations in a simplified reed musical instrument model: Bouasse-Benade prescription assessed through numerical continuation

Acta Acustica ◽  
2020 ◽  
Vol 4 (6) ◽  
pp. 27
Author(s):  
Joel Gilbert ◽  
Sylvain Maugeais ◽  
Christophe Vergez
Keyword(s):  
Dynamical System ◽  
Continuation Method ◽  
Nonlinear Dynamical System ◽  
Period Doubling ◽  
Acoustic Resonance ◽  
Musical Instrument ◽  
Numerical Continuation ◽  
Physical Parameters ◽  
Periodic Oscillations ◽  
Nonlinear Dynamical

A reed instrument model with N acoustical modes can be described as a 2N dimensional autonomous nonlinear dynamical system. Here, a simplified model of a reed-like instrument having two quasi-harmonic resonances, represented by a four dimensional dynamical system, is studied using the continuation and bifurcation software AUTO. Bifurcation diagrams of equilibria and periodic solutions are explored with respect to the blowing mouth pressure, with focus on amplitude and frequency evolutions along the different solution branches. Equilibria and periodic regimes are connected through Hopf bifurcations, which are found to be direct or inverse depending on the physical parameters values. Emerging periodic regimes mainly supported by either the first acoustic resonance (first register) or the second acoustic resonance (second register) are successfully identified by the model. An additional periodic branch is also found to emerge from the branch of the second register through a period-doubling bifurcation. The evolution of the oscillation frequency along each branch of the periodic regimes is also predicted by the continuation method. Stability along each branch is computed as well. Some of the results are interpreted in terms of the ease of playing of the reed instrument. The effect of the inharmonicity between the first two impedance peaks is observed both when the amplitude of the first is greater than the second, as well as the inverse case. In both cases, the blowing pressure that results in periodic oscillations has a lowest value when the two resonances are harmonic, a theoretical illustration of the Bouasse-Benade prescription.

Nonlinear Behavior Analysis of a Rotor Supported on Fluid-Film Bearings

2005 ◽  
Vol 128 (1) ◽  
pp. 35-40 ◽  
Author(s):  
Guangyan Shen ◽  
Zhonghui Xiao ◽  
Wen Zhang ◽  
Tiesheng Zheng
Keyword(s):  
Behavior Analysis ◽  
Dynamical Behavior ◽  
Nonlinear Behavior ◽  
Fluid Film ◽  
Diagnostic Tools ◽  
Nonlinear Phenomena ◽  
Frequency Spectra ◽  
Nonlinear Dynamical ◽  
Synchronous Motion ◽  
Period Motion

A fast and accurate model to calculate the fluid-film forces of a fluid-film bearing with the Reynolds boundary condition is presented in the paper by using the free boundary theory and the variational method. The model is applied to the nonlinear dynamical behavior analysis of a rigid rotor in the elliptical bearing support. Both balanced and unbalanced rotors are taken into consideration. Numerical simulations show that the balanced rotor undergoes a supercritical Hopf bifurcation as the rotor spin speed increases. The investigation of the unbalanced rotor indicates that the motion can be a synchronous motion, subharmonic motion, quasi-period motion, or chaotic motion at different rotor spin speeds. These nonlinear phenomena are investigated in detail. Poincaré maps, bifurcation diagram and frequency spectra are utilized as diagnostic tools.

scholarly journals Combined Structural and Voltage Control of Giant Nonlinearities in Semiconductor Superlattices

Nanomaterials ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 1287
Author(s):  
Mauro Fernandes Pereira ◽  
Apostolos Apostolakis
Keyword(s):  
High Harmonic ◽  
Nonlinear Behavior ◽  
Voltage Control ◽  
High Order ◽  
Strong Increase ◽  
Semiconductor Superlattices ◽  
Fundamental Physics ◽  
Strongly Nonlinear ◽  
Complex Scenario ◽  
Even Harmonics

Recent studies have predicted a strong increase in high harmonic emission in unbiased semiconductor superlattices due to asymmetric current flow. In parallel, an external static bias has led to orders of magnitude control of high harmonics. Here, we study how this control can affect the operation of superlattice multipliers in a range of input frequencies and powers delivered by commercially available GHz sources. We show that the strongly nonlinear behavior can lead to a very complex scenario. Furthermore, it is natural to ask what happens when we combine both asymmetry and voltage control effects. This question is answered by the simulations presented in this study. The efficiency of high-order even harmonics is increased by the combined effects. Furthermore, the development of ‘petals’ in high-order emission is shown to be more easily achieved, opening the possibility to very interesting fundamental physics studies and more efficient devices for the GHz–THz range.

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