Search results for " DYNAMICAL SYSTEM"
showing 10 items of 188 documents
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.
Experimental and numerical enhancement of Vibrational Resonance in a neural circuit
2012
International audience; A neural circuit exactly ruled by the FitzHugh-Nagumo equations is excited by a biharmonic signal of frequencies f and F with respective amplitudes A and B. The magnitude spectrum of the circuit response is estimated at the low frequency driving f and presents a resonant behaviour versus the amplitude B of the high frequency. For the first time, it is shown experimentally that this Vibrational Resonance effect is much more pronounced when the two frequencies are multiple. This novel enhancement is also confirmed by numerical predictions. Applications of this nonlinear effect to the detection of weak stimuli are finally discussed.
A Symplectic Kovacic's Algorithm in Dimension 4
2018
Let $L$ be a $4$th order differential operator with coefficients in $\mathbb{K}(z)$, with $\mathbb{K}$ a computable algebraically closed field. The operator $L$ is called symplectic when up to rational gauge transformation, the fundamental matrix of solutions $X$ satisfies $X^t J X=J$ where $J$ is the standard symplectic matrix. It is called projectively symplectic when it is projectively equivalent to a symplectic operator. We design an algorithm to test if $L$ is projectively symplectic. Furthermore, based on Kovacic's algorithm, we design an algorithm that computes Liouvillian solutions of projectively symplectic operators of order $4$. Moreover, using Klein's Theorem, algebraic solution…
Tame dynamics and robust transitivity
2011
One main task of smooth dynamical systems consists in finding a good decomposition into elementary pieces of the dynamics. This paper contributes to the study of chain-recurrence classes. It is known that $C^1$-generically, each chain-recurrence class containing a periodic orbit is equal to the homoclinic class of this orbit. Our result implies that in general this property is fragile. We build a C1-open set U of tame diffeomorphisms (their dynamics only splits into finitely many chain-recurrence classes) such that for any diffeomorphism in a C-infinity-dense subset of U, one of the chain-recurrence classes is not transitive (and has an isolated point). Moreover, these dynamics are obtained…
Statistical consequences of the Devroye inequality for processes. Applications to a class of non-uniformly hyperbolic dynamical systems
2005
In this paper, we apply Devroye inequality to study various statistical estimators and fluctuations of observables for processes. Most of these observables are suggested by dynamical systems. These applications concern the co-variance function, the integrated periodogram, the correlation dimension, the kernel density estimator, the speed of convergence of empirical measure, the shadowing property and the almost-sure central limit theorem. We proved in \cite{CCS} that Devroye inequality holds for a class of non-uniformly hyperbolic dynamical systems introduced in \cite{young}. In the second appendix we prove that, if the decay of correlations holds with a common rate for all pairs of functio…
Information Decomposition in Bivariate Systems: Theory and Application to Cardiorespiratory Dynamics
2015
In the framework of information dynamics, the temporal evolution of coupled systems can be studied by decomposing the predictive information about an assigned target system into amounts quantifying the information stored inside the system and the information transferred to it. While information storage and transfer are computed through the known self-entropy (SE) and transfer entropy (TE), an alternative decomposition evidences the so-called cross entropy (CE) and conditional SE (cSE), quantifying the cross information and internal information of the target system, respectively. This study presents a thorough evaluation of SE, TE, CE and cSE as quantities related to the causal statistical s…
Structure of equilibrium states on self-affine sets and strict monotonicity of affinity dimension
2016
A fundamental problem in the dimension theory of self‐affine sets is the construction of high‐dimensional measures which yield sharp lower bounds for the Hausdorff dimension of the set. A natural strategy for the construction of such high‐dimensional measures is to investigate measures of maximal Lyapunov dimension; these measures can be alternatively interpreted as equilibrium states of the singular value function introduced by Falconer. While the existence of these equilibrium states has been well known for some years their structure has remained elusive, particularly in dimensions higher than two. In this article we give a complete description of the equilibrium states of the singular va…
Information Dynamics of Electric Field Intensity before and during the COVID-19 Pandemic.
2022
This work investigates the temporal statistical structure of time series of electric field (EF) intensity recorded with the aim of exploring the dynamical patterns associated with periods with different human activity in urban areas. The analyzed time series were obtained from a sensor of the EMF RATEL monitoring system installed in the campus area of the University of Novi Sad, Serbia. The sensor performs wideband cumulative EF intensity monitoring of all active commercial EF sources, thus including those linked to human utilization of wireless communication systems. Monitoring was performed continuously during the years 2019 and 2020, allowing us to investigate the effects on the patterns…
Identification of Replicator Mutator models
2006
The complexity of biology literally calls for quantitative tools in order to support and validate biologists intuition and traditional qualitative descriptions. In this paper, the Replicator-Mutator models for Evolutionary Dynamics are validated/invalidated in a worst-case deterministic setting. These models analyze the DNA and RNA evolution or describe the population dynamics of viruses and bacteria. We identify the Fitness and the Replication Probability parameters of a genetic sequences, subject to a set of stringent constraints to have physical meaning and to guarantee positiveness. The conditional central estimate is determined in order to validate/invalidate the model. The effectivene…
The case of equality in the dichotomy of Mohammadi-Oh
2017
If $n \geq 3$ and $\Gamma$ is a convex-cocompact Zariski-dense discrete subgroup of $\mathbf{SO}^o(1,n+1)$ such that $\delta_\Gamma=n-m$ where $m$ is an integer, $1 \leq m \leq n-1$, we show that for any $m$-dimensional subgroup $U$ in the horospheric group $N$, the Burger-Roblin measure associated to $\Gamma$ on the quotient of the frame bundle is $U$-recurrent.