Corpus ID: 119197295

A unified theory of chaos linking nonlinear dynamics and statistical physics

@article{Poon2010AUT,
  title={A unified theory of chaos linking nonlinear dynamics and statistical physics},
  author={Chi-Sang Poon and Cheng Li and Guo-qiang Wu},
  journal={arXiv: Chaotic Dynamics},
  year={2010}
}
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene expression or stock exchange to quantum chaos. Traditionally, deterministic chaos is characterized by "sensitive dependence on initial conditions" as indicated by a positive Lyapunov exponent. However, ambiguity arises when applying this criterion to real-world data… Expand
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References

SHOWING 1-10 OF 49 REFERENCES
Can noise induce chaos
An important component of the mathematical definition of chaos is sensitivity to initial conditions. Sensitivity to initial conditions is usually measured in a deterministic model by the dominantExpand
Ergodic theory of chaos and strange attractors
Physical and numerical experiments show that deterministic noise, or chaos, is ubiquitous. While a good understanding of the onset of chaos has been achieved, using as a mathematical tool theExpand
Noise-induced unstable dimension variability and transition to chaos in random dynamical systems.
TLDR
Results are reported concerning the transition to chaos in random dynamical systems where a periodic attractor coexists with a nonattracting chaotic saddle, which can be expected in any periodic window of a nonlinear dynamical system. Expand
Titration of chaos with added noise
TLDR
It is shown that the controlled addition of white or colored noise to a signal with a preexisting noise floor results in a titration index that faithfully tracks the onset of deterministic chaos in all standard bifurcation routes to chaos and gives a relative measure of chaos intensity. Expand
Detection of nonlinear dynamics in short, noisy time series
TLDR
A computational procedure is presented, based on a comparison of the prediction power of linear and nonlinear models of the Volterra–Wiener form, which is capable of robust and highly sensitive statistical detection of deterministic dynamics, including chaotic dynamics, in experimental time series. Expand
On Nonlinear, Stochastic Dynamics in Economic and Financial Time Series
The search for deterministic chaos in economic and financial time series has attracted much interest over the past decade. Evidence of chaotic structures is usually blurred, however, by large randomExpand
Chaotic mixing in noisy Hamiltonian systems
This paper summarizes an investigation of the effects of low-amplitude noise and periodic driving on phase-space transport in three-dimensional Hamiltonian systems, a problem directly applicable toExpand
Distinguishing between low-dimensional dynamics and randomness in measured time series
The success of current attempts to distinguish between low-dimensional chaos and random behavior in a time series of observations is considered. First we discuss stationary stochastic processes whichExpand
When can noise induce chaos and why does it matter: a critique
TLDR
Using theoretical models and empirical data on microtine rodent cycles and laboratory populations of Tribolium, it is illustrated how data analyses focusing on attributes of the skeleton and its attractor – such as the “deterministic Lyapunov exponent”λ0 that Dennis et al. have used as their primary indicator of chaos – will frequently give misleading results. Expand
Chaos, Strange Attractors, and Fractal Basin Boundaries in Nonlinear Dynamics
TLDR
Basic developments in the field of chaotic dynamics of dissipative systems are reviewed, Topics covered include strange attractors, how chaos comes about with variation of a system parameter, universality, fractal basin boundaries and their effect on predictability, and applications to physical systems. Expand
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