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A pure and incompressible material is confined between two plates such that it is heated from below and cooled from above. When its melting temperature is comprised between these two imposed temperatures, an interface separating liquid and…
In this paper is studied the behavior of lines of curvature near umbilic points that appear generically on surfaces depending on two parameters.
A taxonomy of large financial crashes proposed in the literature locates the burst of speculative bubbles due to endogenous causes in the framework of extreme stock market crashes, defined as falls of market prices that are outlier with…
As the parameters of a piecewise-smooth system of ODEs are varied, a periodic orbit undergoes a bifurcation when it collides with a surface where the system is discontinuous. Under certain conditions this is a grazing-sliding bifurcation.…
Motivation: Many biochemical pathways are known, but the numerous parameters required to correctly explore the dynamics of the pathways are not known. For this reason, algorithms that can make inferences by looking at the topology of a…
For a discrete dynamical system on $\R$ generated by a quadratic function, we show, using elementary computations, that the existence, number, and stability of 3-cycles are determined by a single parameter depending on the coefficients of…
There are few examples of non-autonomous vector fields exhibiting complex dynamics that may be proven analytically. We analyse a family of periodic perturbations of a weakly attracting robust heteroclinic network defined on the two-sphere.…
Decay to asymptotic steady state in one-dimensional logistic-like mappings is characterized by considering a phenomenological description supported by numerical simulations and confirmed by a theoretical description. As the control…
We study the bifurcations and the chaotic behaviour of a periodically forced double-well Duffing oscillator coupled to a single-well Duffing oscillator. Using the amplitude and the frequency of the driving force as control parameters, we…
A family of periodic perturbations of an attracting robust heteroclinic cycle defined on the two-sphere is studied by reducing the analysis to that of a one-parameter family of maps on a circle. The set of zeros of the family forms a…
A well-known model due to J.-M. Lasry and P.L. Lions that presents the evolution of prices in a market as the evolution of a free boundary in a diffusion equation is suggested to be modified in order to show instabilities for some values of…
We consider the free boundary problem for a liquid drop of nearly spherical shape with capillarity, and we study the existence of nontrivial (i.e., non spherical) rotating traveling profiles bifurcating from the spherical shape, where the…
The MHD flow driven by a travelling magnetic field (TMF) in an annular channel is investigated numerically. For sufficiently large magnetic Reynolds number Rm, or if a large enough pressure gradient is externally applied, the system…
Matrix stiffness expressions are derived for the particle movements in an assembly of rigid granules having compliant contacts. The derivations include stiffness terms that arise from the particle shapes at their contacts. These geometric…
The phenomenon of turbulence is investigated in the context of globally coupled maps. The local dynamics is given by the Chat\'e-Manneville minimal map previously used in studies of spatiotemporal intermittency in locally coupled map…
We investigate the evaporation of a two-dimensional droplet on a solid surface. The solid is flat but with smooth chemical variations that lead to a space-dependent local contact angle. We perform a detailed bifurcation analysis of the…
We consider the demixing of a binary fluid mixture, under gravity, which is steadily driven into a two phase region by slowly ramping the temperature. We assume, as a first approximation, that the system remains spatially isothermal, and…
As parameters are varied a boundary equilibrium bifurcation (BEB) occurs when an equilibrium collides with a discontinuity surface in a piecewise-smooth system of ODEs. Under certain genericity conditions, at a BEB the equilibrium either…
Spin relaxation in a strong-coupling regime (with respect to the spin system) is investigated in detail based on the spin-boson model in a stochastic limit. We find a bifurcation phenomenon in temperature dependence of relaxation constants,…
The aim of this paper (inspired from a problem of Habegger) is to describe the set of cubical decompositions of compact manifolds mod out by a set of combinatorial moves analogous to the bistellar moves considered by Pachner, which we call…