Search results for "Chaotic"
showing 10 items of 297 documents
On lower-bound estimates of the Lyapunov dimension and topological entropy for the Rossler systems
2019
In this paper, on the example of the Rössler systems, the application of the Pyragas time-delay feedback control technique for verification of Eden’s conjecture on the maximum of local Lyapunov dimension, and for the estimation of the topological entropy is demonstrated. To this end, numerical experiments on computation of finite-time local Lyapunov dimensions and finite-time topological entropy on a Rössler attractor and embedded unstable periodic orbits are performed. The problem of reliable numerical computation of the mentioned dimension-like characteristics along the trajectories over large time intervals is discussed. peerReviewed
All-fiber based chaotic polarization scrambler
2014
We present a fiber-based polarization scrambler founded on the nonlinear interaction between a signal and its backward replica generated and amplified by a reflective loop. The output polarization dynamic turns out to be chaotic.
Were the chaotic ELMs in TCV the result of an ARMA process?
2004
The results of a previous paper claiming the demonstration that edge localized mode (ELM) dynamics on TCV are chaotic in a number of cases has recently been called into question, because the statistical test employed was found to also identify linear auto regressive—moving average (ARMA) models as chaotic. The TCV ELM data has therefore been re-examined with an improved method that is able to make this distinction, and the ARMA model is found to be an inappropriate description of the dynamics on TCV. The hypothesis that ELM dynamics are chaotic on TCV in a number of cases is therefore still favoured.
Semipredictable dynamical systems
2015
A new class of deterministic dynamical systems, termed semipredictable dynamical systems, is presented. The spatiotemporal evolution of these systems have both predictable and unpredictable traits, as found in natural complex systems. We prove a general result: The dynamics of any deterministic nonlinear cellular automaton (CA) with $p$ possible dynamical states can be decomposed at each instant of time in a superposition of $N$ layers involving $p_{0}$, $p_{1}$,... $p_{N-1}$ dynamical states each, where the $p_{k\in \mathbb{N}}$, $k \in [0, N-1]$ are divisors of $p$. If the divisors coincide with the prime factors of $p$ this decomposition is unique. Conversely, we also prove that $N$ CA w…
Combined impacts of the Allee effect, delay and stochasticity: Persistence analysis
2020
Abstract We study a combined influence of the Allee effect, delay and stochasticity on the base of the phenomenological Hassell mathematical model of population dynamics. This bistable dynamical model possesses a wide variety of regimes, both regular and chaotic. In the persistence zone, these regimes coexist with the trivial equilibrium that corresponds to the extinction of the population. It is shown that borders of the persistence zone are defined by the crisis and saddle-node bifurcation points. Noise-induced transitions from the persistence to the extinction are studied both numerically and analytically. Using numerical modeling, we have found that the persistence zone can decrease and…
Random bit generation through polarization chaos in nonlinear optical fibers
2017
Nowadays, cryptographic applications are becoming of paramount importance in order to guarantee ultimately secure communications. Performances of classical and quantum key distribution and encryption algorithms are strongly dependent on the used Random Number Generator (RNG). A good RNG must produce unpredictable, unreproducible and unbiased sequences of numbers. For this reason, many true random number generators relying on chaotic physical phenomena, such as chaotic oscillations of high-bandwidth lasers [1, 2] or polarization chaos from a VCSEL diode [3], have been developed. In this work, we propose a RNG implementation based on a different physical mechanism than the ones previously use…
"Table 1" of "Comprehensive measurements of $t$-channel single top-quark production cross sections at $\sqrt{s} = 7$ TeV with the ATLAS detector"
2014
Predicted and observed events yields for the 2-jet and 3-jet channels considered in this measurement. The multijet background is estimated using data-driven techniques (see Sec. VB); an uncertainty of $50\%$ is applied. All the other expectations are derived using theoretical cross sections and their uncertainties (see Secs. VA and VC in the paper).
Coexistence of periods in a bifurcation
2012
Abstract A particular type of order-to-chaos transition mediated by an infinite set of coexisting neutrally stable limit cycles of different periods is studied in the Varley–Gradwell–Hassell population model. We prove by an algebraic method that this kind of transition can only happen for a particular bifurcation parameter value. Previous results on the structure of the attractor at the transition point are here simplified and extended.
Complex Dynamics in a Harmonically Excited Lennard-Jones Oscillator: Microcantilever-Sample Interaction in Scanning Probe Microscopes1
1998
In this paper we model the microcantilever-sample interaction in an atomic force microscope (AFM) via a Lennard-Jones potential and consider the dynamical behavior of a harmonically forced system. Using nonlinear analysis techniques on attracting limit sets, we numerically verify the presence of chaotic invariant sets. The chaotic behavior appears to be generated via a cascade of period doubling, whose occurrence has been studied as a function of the system parameters. As expected, the chaotic attractors are obtained for values of parameters predicted by Melnikov theory. Moreover, the numerical analysis can be fruitfully employed to analyze the region of the parameter space where no theoret…
Transitions in a stratified Kolmogorov flow
2016
We study the Kolmogorov flow with weak stratification. We consider a stabilizing uniform temperature gradient and examine the transitions leading the flow to chaotic states. By solving the equations numerically we construct the bifurcation diagram describing how the Kolmogorov flow, through a sequence of transitions, passes from its laminar solution toward weakly chaotic states. We consider the case when the Richardson number (measure of the intensity of the temperature gradient) is $$Ri=10^{-5}$$ , and restrict our analysis to the range $$0<Re<30$$ . The effect of the stabilizing temperature is to shift bifurcation points and to reduce the region of existence of stable drifting states. The…