Search results for "chaos"

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…

Multiple job holding, societal change, and individual careers: Contributions to the chaos theory of careers

2020

The chaos theory of careers was applied to identify the connections between multiple jobholders’ careers and societal change. Multiple job holding is a form of employment that consists of two or more overlapping jobs. Six interviews with men born in the 1960s in Finnish North Karelia, whose multiple job holding included agricultural and forestry work, were analyzed. Our results showed that multiple job holding career development has societal connections and that the experiences of multiple job holding varied across individuals. Moreover, multiple job holding experiences and further career development endeavors were influenced by whether the multiple job holding career developed in line wit…

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…

Control of irregular cardiac rhythm

2018

International audience; The aim of this work is to investigate the chaos control of the one di- mensional map which modelizes the duration of the current cardiac action potential (APD) as a function of the previous one. Using OGY control method, we obtain very satisfactory numerical results to stabilize the irregular heart rhythm into the normal rhythm.

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…

Bicausative matrices to measure structural change: Are they a good tool?

1999

The causative-matrix method to analyze temporal change assumes that a matrix transforms one Markovian transition matrix into another by a left multiplication of the first matrix; the method is demand-driven when applied to input-output economics. An extension is presented without assuming the demand-driven or supply-driven hypothesis. Starting from two flow matrices X and Y, two diagonal matrices are searched, one premultiplying and the second postmultiplying X, to obtain a result the closer as possible to Y by least squares. The paper proves that the method is deceptive because the diagonal matrices are unidentified and the interpretation of results is unclear. Keywords : Input-Output ; Ch…

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 $\ensuremath{\pi}$.

Experimental study of electrical FitzHugh-Nagumo neurons with modified excitability

2006

International audience; We present an electronical circuit modelling a FitzHugh-Nagumo neuron with a modified excitability. To characterize this basic cell, the bifurcation curves between stability with excitation threshold, bistability and oscillations are investigated. An electrical circuit is then proposed to realize a unidirectional coupling between two cells, mimicking an inter-neuron synaptic coupling. In such a master-slave configuration, we show experimentally how the coupling strength controls the dynamics of the slave neuron, leading to frequency locking, chaotic behavior and synchronization. These phenomena are then studied by phase map analysis. The architecture of a possible ne…

Predictability, chaos and coordination in bird vigilant behaviour

1999

Revisiting Bicausative Matrices: The Swiss Cheese of Chaos

2009

This paper returns to de Mesnard's paper of 2000, which has exposed the so-called method of bicausative matrices. This method was created to analyze the structural change between two matrices, as an improvement of the causative method of Jackson and al. (1990). In its 2000 paper, de Mesnard has shown that chaos affects the bicausative method: two solutions are found with a brutal switching between both. This new paper demonstrates that the chaos can be largely circumvented, is essentially localized in a small interval and is only a transitory effect between two non-chaotic "regimes", is not always observed, is limited to relatively small matrices.