Search results for "bifurcations"

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…

Theoretical conditions for the coexistence of viral strains with differences in phenotypic traits : A bifurcation analysis

2019

We investigate the dynamics of a wild-type viral strain which generates mutant strains differing in phenotypic properties for infectivity, virulence and mutation rates. We study, by means of a mathematical model and bifurcation analysis, conditions under which the wild-type and mutant viruses, which compete for the same host cells, can coexist. The coexistence conditions are formulated in terms of the basic reproductive numbers of the strains, a maximum value of the mutation rate and the virulence of the pathogens. The analysis reveals that parameter space can be divided into five regions, each with distinct dynamics, that are organized around degenerate Bogdanov–Takens and zero-Hopf bifurc…

Modelling temperature-dependent dynamics of single and mixed infections in a plant virus

2022

Multiple viral infection is an important issue in health and agriculture with strong impacts on society and the economy. Several investigations have dealt with the population dynamics of viruses with different dynamic properties, focusing on strain competition during multiple infections and the effects on viruses’ hosts. Recent interest has been on how multiple infections respond to abiotic factors such as temperature (T). This is especially important in the case of plant pathogens, whose dynamics could be affected significantly by global warming. However, few mathematical models incorporate the effect of T on parasite fitness, especially in mixed infections. Here, we investigate simple mat…

MR3090050 Reviewed Belabbas, Mohamed Ali On global stability of planar formations. IEEE Trans. Automat. Control 58 (2013), no. 8, 2148–2153. (Reviewe…

2014

The focus of the paper is planar formation control, i.e. the design of control laws to stabilize agents at given distances from each other, under the constraint that the dynamics of each agent only depends on a subset of the other agents. The main contribution of the paper is the following: It is shown that a simple four-agent formation cannot be globally stabilized using twice differentiable control laws (this is not the case for three-agent formations), even up to sets of measure zero of initial conditions. This suggests that for four-agent formations one needs to look for control laws that are either not differentiable (or even not continuous) or of higher order in the dynamics. The appr…

Attracteurs et bifurcations en dynamique holomorphe

2019

Modified post-bifurcation dynamics and routes to chaos from double-Hopf bifurcations in a hyperchaotic system

2012

In order to understand the onset of hyperchaotic behavior recently observed in many systems, we study bifurcations in the modified Chen system leading from simple dynamics into chaotic regimes. In particular, we demonstrate that the existence of only one fixed point of the system in all regions of parameter space implies that this simple point attractor may only be destabilized via a Hopf or double Hopf bifurcation as system parameters are varied. Saddle-node, transcritical and pitchfork bifurcations are precluded. The normal form immediately following double Hopf bifurcations is constructed analytically by the method of multiple scales. Analysis of this generalized double Hopf normal form …

Mixed-mode oscillation-incrementing bifurcations and a devil’s staircase from a nonautonomous, constrained Bonhoeffer-van der Pol oscillator

2018

Blenders near polynomial product maps of $\mathbb C^2$

2021

In this paper we show that if $p$ is a polynomial which bifurcates then the product map $(z,w)\mapsto(p(z),q(w))$ can be approximated by polynomial skew products possessing special dynamical objets called blenders. Moreover, these objets can be chosen to be of two types : repelling or saddle. As a consequence, such product map belongs to the closure of the interior of two different sets : the bifurcation locus of $H_d(\mathbb P^2)$ and the set of endomorphisms having an attracting set of non-empty interior. In an independent part, we use perturbations of H\'enon maps to obtain examples of attracting sets with repelling points and also of quasi-attractors which are not attracting sets.

Bifurcations of links of periodic orbits in non-singular Morse–Smale systems with a rotational symmetry on S3

2000

Abstract In this paper we consider a rotational symmetry on a non-singular Morse–Smale (NMS) system analyzing the restrictions this symmetry imposes on the links defined by the set of its periodic orbits and to the appearance of local generic codimension one bifurcations in the set of NMS flows on S 3 . The topological characterization is obtained by writing the involved links in terms of Wada operations. It is also obtained that symmetry implies that in general bifurcations have to be multiple. On the other hand, we also see that there exists a set of links that cannot be related to any other by sequences of this kind of bifurcation.

Paysages et choix d'itinéraires pédestres en milieu urbain. Une nouvelle approche par les bifurcations

2007

Walking has long been neglected in urban mobility research. In the context of a sustainable mobility, it is now included into numerous works including various approaches. The well-known models of flows affectation are often used to study the behaviour of pedestrians and to identify their preferences. However, the factors that are usually chosen to describe the urban environment are usually limited or inappropriate to the pedestrian movement. In addition, these models assume that the choices made by pedestrians are predetermined at the start of each trip, without any possible decision intervening along these trips. In this paper, we propose to test the role of urban landscape by using a new …