Search results for " DYNAMICAL SYSTEM"

Darboux integrable system with a triple point and pseudo-abelian integrals

2016

We study pseudo-abelian integrals associated with polynomial perturbations of Dar-boux integrable system with a triple point. Under some assumptions we prove the local boundedness of the number of their zeros. Assuming that this is the only non-genericity, we prove that the number of zeros of the corresponding pseudo-abelian integrals is bounded uniformly for nearby Darboux integrable foliations.

A Hybrid Control Strategy for Quadratic Boost Converters with Inductor Currents Estimation

2020

International audience; This paper deals with a control strategy for a DC-DC quadratic boost converter. In particular, a hybrid control scheme is proposed to encompass a control law and an observer for the estimation of the system states, based only on the measurements of the input and output voltages. Differently from classical control methods, where the controller is designed from a small-signal model, here the real model of the system is examined without considering the average values of the discrete variables. Using hybrid dynamical system theory, asymptotic stability of a neighborhood of the equilibrium point is established, ensuring practical stability of the origin, which contains es…

On a Planar Dynamical System Arising in the Network Control Theory

2016

We study the structure of attractors in the two-dimensional dynamical system that appears in the network control theory. We provide description of the attracting set and follow changes this set suffers under the changes of positive parameters µ and Θ.

Multiple steady states and the form of response functions to antigen in a model for the initiation of T cell activation

2017

The aim of this paper is to study the qualitative behaviour predicted by a mathematical model for the initial stage of T-cell activation. The state variables in the model are the concentrations of phosphorylation states of the T-cell receptor (TCR) complex and the phosphatase SHP-1 in the cell. It is shown that these quantities cannot approach zero and that the model possesses more than one positive steady state for certain values of the parameters. It can also exhibit damped oscillations. It is proved that the chemical concentration which represents the degree of activation of the cell, that of the maximally phosphorylated form of the TCR complex, is, in general, a non-monotone function of…

Viral replication modes in single-peak fitness landscapes: A dynamical systems analysis

2017

Positive-sense, single-stranded RNA viruses are important pathogens infecting almost all types of organisms. Experimental evidence from distributions of mutations and from viral RNA amplification suggest that these pathogens may follow different RNA replication modes, ranging from the stamping machine replication (SMR) to the geometric replication (GR) mode. Although previous theoretical work has focused on the evolutionary dynamics of RNA viruses amplifying their genomes with different strategies, little is known in terms of the bifurcations and transitions involving the so-called error threshold (mutation-induced dominance of mutants) and lethal mutagenesis (extinction of all sequences du…

Sustained oscillations in the MAP kinase cascade.

2016

Abstract The MAP kinase cascade is a network of enzymatic reactions arranged in layers. In each layer occurs a multiple futile cycle of phosphorylations. The fully phosphorylated substrate then serves as an enzyme for the layer below. This paper focuses on the existence of parameters for which Hopf bifurcations occur and generate periodic orbits. Furthermore it is explained how geometric singular perturbation theory allows to generalize results from simple models to more complex ones.

EMERGENCE: WHAT DOES IT MEAN AND HOW IS IT RELEVANT TO COMPUTER ENGINEERING?

2018

A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class

2022

We give a $C^1$-perturbation technique for ejecting an a priori given finite set of periodic points preserving a given finite set of homo/hetero-clinic intersections from a chain recurrence class of a periodic point. The technique is first stated under a simpler setting called Markov iterated function system, a two dimensional iterated function system in which the compositions are chosen in Markovian way. Then we apply the result to the setting of three dimensional partially hyperbolic diffeomorphisms.

Existence de points fixes enlacés à une orbite périodique d'un homéomorphisme du plan

1992

Let f be an orientation-preserving homeomorphism of the plane such that f-Id is contracting. Under these hypotheses, we establish the existence, for every periodic orbit, of a fixed point which has nonzero linking number with this periodic orbit.

STABILITY OF A STOCHASTICALLY PERTURBED MODEL OF INTRACELLULAR SINGLE-STRANDED RNA VIRUS REPLICATION

2019

Compared to the replication of double-stranded RNA and DNA viruses, the replication of single-stranded viruses requires the production of a number of intermediate strands that serve as templates for the synthesis of genomic-sense strands. Two theoretical extreme mechanisms for replication for such single-stranded viruses have been proposed; one extreme being represented by the so-called linear stamping machine and the opposite extreme by the exponential growth. Of course, real systems are more complex and examples have been described in which a combination of such extreme mechanisms can also occur: a fraction of the produced progeny resulting from a stamping-machine type of replication that…