754 research outputs found
On the assignability of regularity coefficients and central exponents of discrete linear time-varying systems
In this paper we investigate the problem of assignability of the so-called regularity coefficients and central exponents of discrete linear time-varying systems. The main result presents a possibility of assignability of Lyapunov, Perron, Grobman regularity coefficients and central exponents by a linear time-varying feedback under the assumptions of uniform complete controllability
A simple method for detecting chaos in nature
Chaos, or exponential sensitivity to small perturbations, appears everywhere
in nature. Moreover, chaos is predicted to play diverse functional roles in
living systems. A method for detecting chaos from empirical measurements should
therefore be a key component of the biologist's toolkit. But, classic
chaos-detection tools are highly sensitive to measurement noise and break down
for common edge cases, making it difficult to detect chaos in domains, like
biology, where measurements are noisy. However, newer tools promise to overcome
these limitations. Here, we combine several such tools into an automated
processing pipeline, and show that our pipeline can detect the presence (or
absence) of chaos in noisy recordings, even for difficult edge cases. As a
first-pass application of our pipeline, we show that heart rate variability is
not chaotic as some have proposed, and instead reflects a stochastic process in
both health and disease. Our tool is easy-to-use and freely available
Synchronization of spatio-temporal chaos as an absorbing phase transition: a study in 2+1 dimensions
The synchronization transition between two coupled replicas of
spatio-temporal chaotic systems in 2+1 dimensions is studied as a phase
transition into an absorbing state - the synchronized state. Confirming the
scenario drawn in 1+1 dimensional systems, the transition is found to belong to
two different universality classes - Multiplicative Noise (MN) and Directed
Percolation (DP) - depending on the linear or nonlinear character of damage
spreading occurring in the coupled systems. By comparing coupled map lattice
with two different stochastic models, accurate numerical estimates for MN in
2+1 dimensions are obtained. Finally, aiming to pave the way for future
experimental studies, slightly non-identical replicas have been considered. It
is shown that the presence of small differences between the dynamics of the two
replicas acts as an external field in the context of absorbing phase
transitions, and can be characterized in terms of a suitable critical exponent.Comment: Submitted to Journal of Statistical Mechanics: Theory and Experimen
Stability, sensitivity and optimisation of chaotic acoustic oscillations
In an acoustic cavity with a heat source, such as a flame in a gas turbine,
the thermal energy of the heat source can be converted into acoustic energy,
which may generate a loud oscillation. If uncontrolled, these nonlinear
acoustic oscillations, also known as thermoacoustic instabilities, can cause
large vibrations up to structural failure. Numerical and experimental studies
showed that thermoacoustic oscillations can be chaotic. It is not yet known,
however, how to minimise such chaotic oscillations. We propose a strategy to
analyse and minimise chaotic acoustic oscillations, for which traditional
stability and sensitivity methods break down. We investigate the acoustics of a
nonlinear heat source in an acoustic resonator. First, we propose covariant
Lyapunov analysis as a tool to calculate the stability of chaotic acoustics
making connections with eigenvalue and Floquet analyses. We show that covariant
Lyapunov analysis is the most general flow stability tool. Second, covariant
Lyapunov vector analysis is applied to a chaotic system. The time-averaged
acoustic energy is investigated by varying the heat-source parameters.
Thermoacoustic systems can display both hyperbolic and non-hyperbolic chaos, as
well as discontinuities in the time-averaged acoustic energy. Third, we embed
sensitivities of the time-averaged acoustic energy in an optimisation routine.
This procedure achieves a significant reduction in acoustic energy and
identifies the bifurcations to chaos.
The analysis and methods proposed enable the reduction of chaotic
oscillations in thermoacoustic systems by optimal passive control. The
techniques presented can be used in other unsteady fluid-dynamics problems with
virtually no modification
The Fermi-Pasta-Ulam problem: 50 years of progress
A brief review of the Fermi-Pasta-Ulam (FPU) paradox is given, together with
its suggested resolutions and its relation to other physical problems. We focus
on the ideas and concepts that have become the core of modern nonlinear
mechanics, in their historical perspective. Starting from the first numerical
results of FPU, both theoretical and numerical findings are discussed in close
connection with the problems of ergodicity, integrability, chaos and stability
of motion. New directions related to the Bose-Einstein condensation and quantum
systems of interacting Bose-particles are also considered.Comment: 48 pages, no figures, corrected and accepted for publicatio
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