Related papers: Integrate-and-fire models with an almost periodic …
The chaotic phenomenon of intermittency is modeled by a simple map of the unit interval, the Farey map. The long term dynamical behaviour of a point under iteration of the map is translated into a spin system via symbolic dynamics. Methods…
The paper studies different variants of almost periodicity notion. We introduce the class of eventually strongly almost periodic sequences where some suffix is strongly almost periodic (=uniformly recurrent). The class of almost periodic…
This book is an extension of my doctoral dissertation, focusing on techniques for analyzing stability (dissipativity) and achieving stabilization of linear systems that are characterized by non-trivial distributed delays. It specifically…
A new functional-based approach is developed for the stability analysis of linear impulsive systems. The new method, which introduces looped-functionals, considers non-monotonic Lyapunov functions and leads to LMIs conditions devoid of…
This note presents an extension to the adaptive control strategy presented in [1] able to counter eventual instability due to disturbances at the input of an otherwise $\mathcal{L}_2$ stable closed-loop system. These disturbances are due to…
Probability density function of output interspike intervals is found in exact form for leaky integrate and fire neuron stimulated with Poisson stream. The diffusion approximation is not exploited.
We study stochastic tree fluid networks driven by a multidimensional Levy process. We are interested in (the joint distribution of) the steady-state content in each of the buffers, the busy periods, and the idle periods. To investigate…
Hitting rate and escape rate are two examples of recurrence laws for a dynamical system, and a general limit connects them. We show that for both Gibbs-Markov systems or any systems with the $\phi$-mixing measure, for a sequence of nested…
In this work it is described how to enhance and generalize the equivalent model (arXiv:0802.0421) of integrate-and-fire dynamics in order to treat any complex neuronal networks, especially those exibiting modular structure. It has been…
We study a class of planar integrate and fire (IF) models called adaptive integrate and fire (AIF) models, which possesses an adaptation variable on top of membrane potential, and whose subthreshold dynamics is piecewise linear (PWL). These…
Leaky integrate-and-fire (LIF) models are mean-field limits, with a large number of neurons, used to describe neural networks. We consider inhomogeneous networks structured by a connec-tivity parameter (strengths of the synaptic weights)…
Drift-diffusion plasma fluid models are commonly used to simulate electric discharges. Such models can computationally be very efficient if they are combined with explicit time integration. This paper deals with two issues that often arise…
We study the heating time in periodically driven $D$-dimensional systems with interactions that decay with the distance $r$ as a power-law $1/r^\alpha$. Using linear response theory, we show that the heating time is exponentially long as a…
Based on the path integral representation of the partition function of a many body system with separable two body interaction we propose a systematic extension of the perturbed static path approximation (PSPA) to lower temperatures.…
In this study, we investigate the ISS of impulsive switched systems that have modes with both stable and unstable flows. We assume that the switching signal satisfies mode-dependent average dwell and leave time conditions. To establish ISS…
We consider a model for chaotic diffusion with amplification on graphs associated with piecewise-linear maps of the interval. We investigate the possibility of having power-law tails in the invariant measure by approximate solution of the…
Low-dimensional dynamical systems are fruitful models for mixing in fluid and granular flows. We study a one-dimensional discontinuous dynamical system (termed "cutting and shuffling" of a line segment), and we present a comprehensive…
We consider a general class of maps of the interval having Lyapunov subexponential instability $|\delta x_{t}|\sim|\delta x_{0}|\exp[\Lambda_{t}(x_{0})\zeta(t)]$, where $\zeta(t)$ grows sublinearly as $t\rightarrow\infty$. We outline here a…
In this work, we investigate the presence of sub-diffusive behavior in the Chirikov-Taylor Standard Map. We show that the stickiness phenomena, present in the mixed phase space of the map setup, can be characterized as a Continuous Time…
In this paper, we discuss the laws of the iterated logarithm (LIL) for occupation times of Markov processes $Y$ in general metric measure space both near zero and near infinity under some minimal assumptions. We first establish LILs of…