2,141 research outputs found
Comparisons between harmonic balance and nonlinear output frequency response function in nonlinear system analysis
By using the Duffing oscillator as a case study, this paper shows that the harmonic components in the nonlinear system response to a sinusoidal input calculated using the Nonlinear Output Frequency Response Functions (NOFRFs) are one of the solutions obtained using the Harmonic Balance Method (HBM). A comparison of the performances of the two methods shows that the HBM can capture the well-known jump phenomenon, but is restricted by computational limits for some strongly nonlinear systems and can fail to provide accurate predictions for some harmonic components. Although the NOFRFs cannot capture the jump phenomenon, the method has few computational restrictions. For the nonlinear damping systems, the NOFRFs can give better predictions for all the harmonic components in the system response than the HBM even when the damping system is strongly nonlinear
Non-linear normal modes (nnms) and their applications in vibration theory: an overview
International audienceThe concept of 'non-linear normal mode' (NNM) is discussed. After providing some introductory definitions, the applications of NNMs to vibration theory are considered. In particular, it is shown how this concept can be used to study forced resonances of non-linear systems and non-linear localisation of vibrational energy in symmetric systems. NNMs can provide a valuable tool for understanding certain essentially non-linear dynamic phenomena that have no counterparts in linear theory and that cannot be analysed by conventional linearised methods. Additional applications of NNMs to modal analysis, model reduction, vibration and shock isolation designs, and the theory of non-linear oscillators are also discussed
Delayed Dynamical Systems: Networks, Chimeras and Reservoir Computing
We present a systematic approach to reveal the correspondence between time
delay dynamics and networks of coupled oscillators. After early demonstrations
of the usefulness of spatio-temporal representations of time-delay system
dynamics, extensive research on optoelectronic feedback loops has revealed
their immense potential for realizing complex system dynamics such as chimeras
in rings of coupled oscillators and applications to reservoir computing.
Delayed dynamical systems have been enriched in recent years through the
application of digital signal processing techniques. Very recently, we have
showed that one can significantly extend the capabilities and implement
networks with arbitrary topologies through the use of field programmable gate
arrays (FPGAs). This architecture allows the design of appropriate filters and
multiple time delays which greatly extend the possibilities for exploring
synchronization patterns in arbitrary topological networks. This has enabled us
to explore complex dynamics on networks with nodes that can be perfectly
identical, introduce parameter heterogeneities and multiple time delays, as
well as change network topologies to control the formation and evolution of
patterns of synchrony
Comparative evaluation of approaches in T.4.1-4.3 and working definition of adaptive module
The goal of this deliverable is two-fold: (1) to present and compare different approaches towards learning and encoding movements us- ing dynamical systems that have been developed by the AMARSi partners (in the past during the first 6 months of the project), and (2) to analyze their suitability to be used as adaptive modules, i.e. as building blocks for the complete architecture that will be devel- oped in the project. The document presents a total of eight approaches, in two groups: modules for discrete movements (i.e. with a clear goal where the movement stops) and for rhythmic movements (i.e. which exhibit periodicity). The basic formulation of each approach is presented together with some illustrative simulation results. Key character- istics such as the type of dynamical behavior, learning algorithm, generalization properties, stability analysis are then discussed for each approach. We then make a comparative analysis of the different approaches by comparing these characteristics and discussing their suitability for the AMARSi project
Hysteresis in Adiabatic Dynamical Systems: an Introduction
We give a nontechnical description of the behaviour of dynamical systems
governed by two distinct time scales. We discuss in particular memory effects,
such as bifurcation delay and hysteresis, and comment the scaling behaviour of
hysteresis cycles. These properties are illustrated on a few simple examples.Comment: 28 pages, 10 ps figures, AMS-LaTeX. This is the introduction of my
Ph.D. dissertation, available at
http://dpwww.epfl.ch/instituts/ipt/berglund/these.htm
Realizing the physics of motile cilia synchronization with driven colloids
Cilia and flagella in biological systems often show large scale cooperative
behaviors such as the synchronization of their beats in "metachronal waves".
These are beautiful examples of emergent dynamics in biology, and are essential
for life, allowing diverse processes from the motility of eukaryotic
microorganisms, to nutrient transport and clearance of pathogens from mammalian
airways. How these collective states arise is not fully understood, but it is
clear that individual cilia interact mechanically,and that a strong and long
ranged component of the coupling is mediated by the viscous fluid. We review
here the work by ourselves and others aimed at understanding the behavior of
hydrodynamically coupled systems, and particularly a set of results that have
been obtained both experimentally and theoretically by studying actively driven
colloidal systems. In these controlled scenarios, it is possible to selectively
test aspects of the living motile cilia, such as the geometrical arrangement,
the effects of the driving profile and the distance to no-slip boundaries. We
outline and give examples of how it is possible to link model systems to
observations on living systems, which can be made on microorganisms, on cell
cultures or on tissue sections. This area of research has clear clinical
application in the long term, as severe pathologies are associated with
compromised cilia function in humans.Comment: 31 pages, to appear in Annual Review of Condensed Matter Physic
Oscillators and relaxation phenomena in Pleistocene climate theory
Ice sheets appeared in the northern hemisphere around 3 million years ago and
glacial-interglacial cycles have paced Earth's climate since then. Superimposed
on these long glacial cycles comes an intricate pattern of millennial and
sub-millennial variability, including Dansgaard-Oeschger and Heinrich events.
There are numerous theories about theses oscillations. Here, we review a number
of them in order to draw a parallel between climatic concepts and dynamical
system concepts, including, in particular, the relaxation oscillator,
excitability, slow-fast dynamics and homoclinic orbits. Namely, almost all
theories of ice ages reviewed here feature a phenomenon of synchronisation
between internal climate dynamics and the astronomical forcing. However, these
theories differ in their bifurcation structure and this has an effect on the
way the ice age phenomenon could grow 3 million years ago. All theories on
rapid events reviewed here rely on the concept of a limit cycle in the ocean
circulation, which may be excited by changes in the surface freshwater surface
balance. The article also reviews basic effects of stochastic fluctuations on
these models, including the phenomenon of phase dispersion, shortening of the
limit cycle and stochastic resonance. It concludes with a more personal
statement about the potential for inference with simple stochastic dynamical
systems in palaeoclimate science.
Keywords: palaeoclimates, dynamical systems, limit cycle, ice ages,
Dansgaard-Oeschger eventsComment: Published in the Transactions of the Philosophical Transactions of
the Royal Society (Series A, Physical Mathematical and Engineering Sciences),
as a contribution to the Proceedings of the workshop on Stochastic Methods in
Climate Modelling, Newton Institute (23-27 August). Philosophical
Transactions of the Royal Society (Series A, Physical Mathematical and
Engineering Sciences), vol. 370, pp. xx-xx (2012); Source codes available on
request to author and on http://www.uclouvain.be/ito
Bifurcation and chaos in the double well Duffing-van der Pol oscillator: Numerical and analytical studies
The behaviour of a driven double well Duffing-van der Pol (DVP) oscillator
for a specific parametric choice () is studied. The
existence of different attractors in the system parameters () domain
is examined and a detailed account of various steady states for fixed damping
is presented. Transition from quasiperiodic to periodic motion through chaotic
oscillations is reported. The intervening chaotic regime is further shown to
possess islands of phase-locked states and periodic windows (including period
doubling regions), boundary crisis, all the three classes of intermittencies,
and transient chaos. We also observe the existence of local-global bifurcation
of intermittent catastrophe type and global bifurcation of blue-sky catastrophe
type during transition from quasiperiodic to periodic solutions. Using a
perturbative periodic solution, an investigation of the various forms of
instablities allows one to predict Neimark instablity in the plane
and eventually results in the approximate predictive criteria for the chaotic
region.Comment: 15 pages (13 figures), RevTeX, please e-mail Lakshmanan for figures,
to appear in Phys. Rev. E. (E-mail: [email protected]
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