Search results for " chaos"
showing 10 items of 70 documents
Discrete spectral incoherent solitons in nonlinear media with noninstantaneous response
2011
International audience; We show theoretically that nonlinear optical media characterized by a finite response time may support the existence of discrete spectral incoherent solitons. The structure of the soliton consists of three incoherent spectral bands that propagate in frequency space toward the low-frequency components in a discrete fashion and with a constant velocity. Discrete spectral incoherent solitons do not exhibit a confinement in the space-time domain, but exclusively in the frequency domain. The kinetic theory describes in detail all the essential properties of discrete spectral incoherent solitons: A quantitative agreement has been obtained between simulations of the kinetic…
Adaptive synchronization of master-slave systems with mixed neutral and discrete time-delays and nonlinear perturbations
2011
This paper investigates the delay-dependent adaptive synchronization problem of the master and slave structure of linear systems with both constant neutral and time-varying discrete time-delays and nonlinear perturbations based on the Barbalat lemma and matching conditions. An adaption law which includes the master-slave parameters is obtained by using the Lyapunov functional method and inequality techniques to synchronize the master-slave systems without the knowledge of upper bounds of perturbation terms. Particularly, it is shown that the synchronization speed can be controlled by adjusting the update gain of the synchronization signal. A numerical example has been given to show the effe…
Uncertainty quantification in simulations of epidemics using polynomial chaos.
2012
Mathematical models based on ordinary differential equations are a useful tool to study the processes involved in epidemiology. Many models consider that the parameters are deterministic variables. But in practice, the transmission parameters present large variability and it is not possible to determine them exactly, and it is necessary to introduce randomness. In this paper, we present an application of the polynomial chaos approach to epidemiological mathematical models based on ordinary differential equations with random coefficients. Taking into account the variability of the transmission parameters of the model, this approach allows us to obtain an auxiliary system of differential equa…
Experimental demonstration of phase bistability in a broad-area optical oscillator with injected signal
2015
We demonstrate experimentally that a broad-area laserlike optical oscillator (a nondegenerate photorefractive oscillator) with structured injected signal displays two-phase patterns. The technique [de Valc\'arcel and Staliunas, Phys. Rev. Lett. 105, 054101 (2010)] consists in spatially modulating the injection, so that its phase alternates periodically between two opposite values, i.e., differing by $\ensuremath{\pi}$.
Noise-induced behavioral change driven by transient chaos
2022
We study behavioral change in the context of a stochastic, non-linear consumption model with preference adjusting, interdependent agents. Changes in long-run consumption behavior are modelled as noise induced transitions between coexisting attractors. A particular case of multistability is considered: two fixed points, whose immediate basins have smooth boundaries, coexist with a periodic attractor, with a fractal immediate basin boundary. If a trajectory leaves an immediate basin, it enters a set of complexly intertwined basins for which final state uncertainty prevails. The standard approach to predicting transition events rooted in the stochastic sensitivity function technique due to Mil…
Pedagogika katolicka – znaczenie i aktualność w kontekście chaosu wartości (perspektywa polska)
2017
Education cannot be reduced to information and should guarantee to the students and their parents the freedom of making axiological decisions and solutions. The above mentioned right is confimed by the right of parents to raise their children according to their own conceptions. In the contemporary chaos of values and principles of education the Catholic education remains a topical, interesting and important proposal for school.
Exchange rates expectations and chaotic dynamics: a replication study
2018
Abstract In this paper the author analyzes the behavior of exchange rates expectations for four currencies, by considering a re-calculation and an extension of Resende and Zeidan (Expectations and chaotic dynamics: empirical evidence on exchange rates, Economics Letters, 2008). Considering Lyapunov exponent-based tests results, they are not supportive of chaos in exchange rates expectations, although the so-called 0–1 test strongly supports the chaos hypothesis.
Chaotic dynamics in an unstirred ferroin catalyzed Belousov–Zhabotinsky reaction
2009
Abstract The Belousov–Zhabotinsky (BZ) reaction is the best known example of far from equilibrium self-organizing chemical reaction. Among the many dynamical behaviors that this reaction can exhibit, spatio-temporal chaos attracted particular interest, both for the ferroin and cerium catalyzed systems. In recent years transient chaos was found in the cerium catalyzed BZ reaction, when conducted in batch and unstirred reactors. It was established that the chaotic oscillations, originated by the coupling among chemical kinetics and transport phenomena, appeared and disappeared following a Ruelle–Takens–Newhouse scenario. In this Letter, we show results about the ferroin catalyzed system condu…