Search results for "Chaotic dynamics"
showing 10 items of 197 documents
Dynamics of a map with a power-law tail
2008
We analyze a one-dimensional piecewise continuous discrete model proposed originally in studies on population ecology. The map is composed of a linear part and a power-law decreasing piece, and has three parameters. The system presents both regular and chaotic behavior. We study numerically and, in part, analytically different bifurcation structures. Particularly interesting is the description of the abrupt transition order-to-chaos mediated by an attractor made of an infinite number of limit cycles with only a finite number of different periods. It is shown that the power-law piece in the map is at the origin of this type of bifurcation. The system exhibits interior crises and crisis-induc…
Damping in quantum love affairs
2011
In a series of recent papers we have used an operatorial technique to describe stock markets and, in a different context, {\em love affairs} and their time evolutions. The strategy proposed so far does not allow any dumping effect. In this short note we show how, within the same framework, a strictly non periodic or quasi-periodic effect can be introduced in the model by describing in some details a linear Alice-Bob love relation with damping.
Bifurcations in the Lozi map
2011
We study the presence in the Lozi map of a type of abrupt order-to-order and order-to-chaos transitions which are mediated by an attractor made of a continuum of neutrally stable limit cycles, all with the same period.
Digit replacement: A generic map for nonlinear dynamical systems
2016
A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical design of useful signals, such as regular or aperiodic oscillations with specific waveforms, the construction of complex attractors with nontrivial properties as well as the coexistence of different basins of attraction in phase space with different qualitative properties. A detailed analysis of the dynamical behavior of the map suggests how the latter can be used in the modeling of complex nonlinear dynamics including, e.g., aperiodic nonchaotic attracto…
Resonance phenomena in a nonlinear neuronal circuit
2015
International audience; We characterizes a nonlinear circuit driven by a bichromatic excitation,that is the sum of two sinusoidal waves with different frequencies f1 and f2 suchthat f2 > f1. Our experiments are confirmed by a numerical analysis of the systemresponse obtained by solving numerically the differential equations which rule thecircuit voltages. Especially, we highlight that the response of the system at the lowfrequency can be optimized by the amplitude of the high frequency. By revisiting thiswell known vibrational resonance effect in the whole amplitude frequency parametricplane, we show experimentally and numerically that a much better resonance can beachieved when the two fre…
COLORED NOISE EFFECTS ON GHOST STOCHASTIC RESONANCE
2014
International audience; We analyze the Ghost Stochastic Resonance (GSR) effect in an electronic circuit exactly ruled by the FitzHugh-Nagumo (FHN) equations, both numerically and experimentally. When the circuit is excited with a bichromatic driving with two close frequencies, we show that for an appropriate noise intensity the circuit response exhibits a ghost frequency which is not present in the biharmonic input signal. In this paper, we highlight the e ects of colored noise on GSR.
A comparative study of noise effects in a FitzHugh-Nagumo circuit
2014
International audience; This paper focuses on the behaviour of a nonlinear FitzHugh-Nagumo circuit in the stochastic case that is in presence of noise and without deterministic driving. When the circuit is tuned below the Andronov-Hopf bifurcation, classical coherence res- onance signature is revealed. We compare the stochastic response of the system when the noise acts on two different parameters of the system. It is experimentally shown that an enhancement of the systems response can be achieved when the noise is directly added into the nonlinearity.
Fractal Weyl law for open quantum chaotic maps
2014
We study the semiclassical quantization of Poincar\'e maps arising in scattering problems with fractal hyperbolic trapped sets. The main application is the proof of a fractal Weyl upper bound for the number of resonances/scattering poles in small domains near the real axis. This result encompasses the case of several convex (hard) obstacles satisfying a no-eclipse condition.
In Vitro Arrhythmia Generation by Mild Hypothermia - a Pitchfork Bifurcation Type Process
2015
International audience; The neurological damage after cardiac arrest (CA) constitutes a big challenge of hospital discharge. The therapeutic hypothermia (34°C-32°C) has shown its benefit to reduce cerebral oxygen demand and improve neurological outcomes after the cardiac arrest. However, it can have many adverse effects, among them the cardiac arrhythmia generation represents an important part (up to 34%, according different clinical studies). Monolayer cardiac culture is prepared with cardiomyocytes from new-born rat directly on the multi-electrodes array, which allows acquiring the extracellular potential of the culture. The temperature range is 37°C - 30°C - 37°C, representing the coolin…
Détection d'Anomalie dans les Signaux Physiologiques
2015
International audience; Les signaux physiologiques sont des séries temporelles riches en informations. Analyser ces signaux pour extraire ces informations, pour établir un diagnostic ou encore pour prédire une évolution, nécessite des outils performants et adaptés à leurs caractéristiques intrinsèques. En effet le comportement d'un système biologique dépend des variations de très nombreux paramètres, ce qui le rend alors presque imprévisible. Les méthodes issues de la théorie du chaos et de la dynamique non linéaire apportent des éléments qui permettent de comprendre ce type de comportements, et d'établir ainsi un lien qualitatif avec des modèles mathématiques bio-inspirés ou phénoménologiq…