Search results for "Nonlinear dynamic"
showing 10 items of 158 documents
Nonlinear dynamical aspects of the human sleep EEG.
1994
This article deals with the application of methods from the theory of nonlinear dynamical systems to EEG signals. Theoretical background, mathematical concepts and algorithms for the calculation of "non-linear parameters" are reviewed and influences of the structure of reconstructed data sets on the calculations are pointed out. We present results for the estimation of the correlation dimension D2 and the principal Lyapunov-exponent lambda 1 for sleep EEG data respectively from 10 and 15 healthy subjects corresponding to different sleep stages. Essentially, we found a statistically significant decrease of both D2 and lambda 1 as sleep moves towards slow wave stages. The values for REM sleep…
Observation of Kuznetsov-Ma soliton dynamics in optical fibre
2012
International audience; The nonlinear Schro¨dinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the physics of extreme waves. However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity. We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important serie…
Dissipative rogue wave generation in multiple-pulsing mode-locked fiber laser
2013
Following the first experimental observation of a new mechanism leading to optical rogue wave (RW) formation briefly reported in Lecaplain et al (2012 Phys. Rev. Lett. 108 233901), we provide an extensive study of the experimental conditions under which these RWs can be detected. RWs originate from the nonlinear interactions of bunched chaotic pulses that propagate in a fiber laser cavity, and manifest as rare events of high optical intensity. The crucial influence of the electrical detection bandwidth is illustrated. We also clarify the observation of RWs with respect to other pulsating regimes, such as Q-switching instability, that also lead to L-shaped probability distribution functions.…
Computer simulations of bioequivalence trials: selection of design and analyte in BCS drugs with first-pass hepatic metabolism: linear kinetics (I).
2008
Modeling and simulation approaches are useful tools to assess the potential outcome of different scenarios in bioequivalence studies. The aim of this study is to propose a new and improved semi-physiological model for bioequivalence trial simulations and apply it for all BCS (Biopharmaceutic Classification System) drug classes with non-saturated first-pass hepatic metabolism. The semi-physiological model was developed in NONMEM VI to simulate bioequivalence trials. Parent drug and metabolite levels for both reference and test were simulated. Eight types of drugs (with high or low permeability and high or low solubility (class I to IV) and high or low intrinsic clearance) were considered in …
Moving mass over a viscoelastic system: asymptotic behaviours and insights into nonlinear dynamics
2023
AbstractMoving masses are of interest in many applications of structural dynamics, soliciting in the last decades a vast debate in the scientific literature. However, despite the attention devoted to the subject, to the best of the authors’ knowledge, there is a lack of analysis about the fate of a movable mass when it rolls or slips with friction on a structure. With the aim of elucidating the dynamics of the simplest paradigm of this system and to investigate its asymptotic response, we make reference to a two-degree-of-freedom model made of an elastically vibrating carriage surmounted by a spherical mass, facing the problem both theoretically and experimentally. In case of linear systems…
Analytical properties of horizontal visibility graphs in the Feigenbaum scenario
2012
Time series are proficiently converted into graphs via the horizontal visibility (HV) algorithm, which prompts interest in its capability for capturing the nature of different classes of series in a network context. We have recently shown [1] that dynamical systems can be studied from a novel perspective via the use of this method. Specifically, the period-doubling and band-splitting attractor cascades that characterize unimodal maps transform into families of graphs that turn out to be independent of map nonlinearity or other particulars. Here we provide an in depth description of the HV treatment of the Feigenbaum scenario, together with analytical derivations that relate to the degree di…
Feigenbaum graphs: a complex network perspective of chaos
2011
The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map…
Incremental dynamic based fragility assessment of reinforced concrete structures: Stationary vs. non-stationary artificial ground motions
2017
Abstract Artificial and natural records are commonly employed by researches and practitioners to perform refined seismic assessments of structures. The techniques for the generation of artificial records and their effectiveness in producing signals which are significantly representative of real earthquakes are still debated as well as results of the consequent seismic assessment to expect from their application. The paper presents an in-depth comparative study highlighting the effect of employing different typologies of artificial ground motion records on seismic assessment results, especially addressing seismic fragility curves. Three sets of 50 stationary, nonstationary evenly modulated a…
Nonlinear control of an activated sludge aeration process: use of fuzzy techniques for tuning PID controllers
1999
In this paper, several tuning algorithms, specifically ITAE, IMC and Cohen and Coon, were applied in order to tune an activated sludge aeration PID controller. Performance results of these controllers were compared by simulation with those obtained by using a nonlinear fuzzy PID controller. In order to design this controller, a trial and error procedure was used to determine, as a function of error at current time and at a previous time, sets of parameters (including controller gain, integral time and derivative time) which achieve satisfactory response of a PID controller actuating over the aeration process. Once these sets of data were obtained, neural networks were used to obtain fuzzy m…
Real-time parameter estimation of Zika outbreaks using model averaging
2017
SUMMARYEarly prediction of the final size of any epidemic and in particular for Zika disease outbreaks can be useful for health authorities in order to plan the response to the outbreak. The Richards model is often been used to estimate epidemiological parameters for arboviral diseases based on the reported cumulative cases in single- and multi-wave outbreaks. However, other non-linear models can also fit the data as well. Typically, one follows the so called post selection estimation procedure, i.e., selects the best fitting model out of the set of candidate models and ignores the model uncertainty in both estimation and inference since these procedures are based on a single model. In this…