Search results for "dynamical system"

On invariant manifolds of saddle points for 3D multistable models

2017

In dynamical systems a particular solution is completely determined by the parameters considered and the initial conditions. Indeed, when the model shows a multistability, starting from different initial state, the trajectories can evolve towards different attractors. The invariant manifolds of the saddle points separate the vector field into the basins of attraction of different stable equilibria. The aim of this work is the reconstruction of these separation surfaces in order to know in advance the geometry of the basins. In this paper three-dimensional models with three or more stable fixed points is investigated. To this purpose a procedure for the detection of the scattered data lying …

ADVANCED MESHLESS NUMERICAL METHODS AND APPLICATIONS

Analysis of the Allee threshold via moving least square approximation

2016

Cooperation is a common behavior between the members of predators species, because it can improve theirs skill in hunt, especially in endangered eco-systems. This behavior it is well known to induce the Strong Allee effect, that can induce the extinction when the initial populations’ is under a critical density called ”Allee threshold ”. Here we investigate the impact of the pack hunting in a predator-prey system in which the predator suffers of an infectious disease with frequency and vertical transmission. The result is a three dimensional system with the predators population divided into susceptible and infected individuals. Studying the system dynamics a scenario was identified in which…

Asymptotic properties of incoherent waves propagating in an all-optical regenerators line

2007

International audience; We present an original method to generate optical pulse trains with random time-interval values from incoherent broadband sources. More precisely, our technique relies on the remarkable properties of a line made of cascaded self-phase modulation-based optical regenerators. Depending on the regenerator parameters, various regimes with noticeably different physical behaviors can be reported.

A proof of bistability for the dual futile cycle

2014

Abstract The multiple futile cycle is an important building block in networks of chemical reactions arising in molecular biology. A typical process which it describes is the addition of n phosphate groups to a protein. It can be modelled by a system of ordinary differential equations depending on parameters. The special case n = 2 is called the dual futile cycle. The main result of this paper is a proof that there are parameter values for which the system of ODE describing the dual futile cycle has two distinct stable stationary solutions. The proof is based on bifurcation theory and geometric singular perturbation theory. An important entity built of three coupled multiple futile cycles is…

Regularity of the Inverse of a Sobolev Homeomorphism

2011

We give necessary and sufficient conditions for the inverse ofa Sobolev homeomorphism to be a Sobolev homeomorphism and conditions under which the inverse is of bounded variation.

Protein aggregation/crystallization and minor structural changes: universal versus specific aspects.

2007

AbstractProtein association covers wide interests in biophysics, protein science, and biotechnologies, and it is often viewed as governed by conformation details. More recently, the existence of a universal physical principle governing aggregation/crystallization processes has been suggested by a series of experiments and shown to be linked to the universal scaling properties of concentration fluctuations occurring in the proximity of a phase transition (spinodal demixing in the specific case). Such properties have provided a quantitative basis for capturing kinetic association data on a universal master curve, ruled by the normalized distance of the state of the system from its instability…

Separatrix reconstruction to identify tipping points in an eco-epidemiological model

2018

Many ecological systems exhibit tipping points such that they suddenly shift from one state to another. These shifts can be devastating from an ecological point of view, and additionally have severe implications for the socio-economic system. They can be caused by overcritical perturbations of the state variables such as external shocks, disease emergence, or species removal. It is therefore important to be able to quantify the tipping points. Here we present a study of the tipping points by considering the basins of attraction of the stable equilibrium points. We address the question of finding the tipping points that lie on the separatrix surface, which partitions the space of system traj…

EMERGENCE OF TRAVELLING WAVES IN SMOOTH NERVE FIBRES

2008

International audience; An approximate analytical solution characterizing initial condi- tions leading to action potential ¯ring in smooth nerve ¯bres is determined, using the bistable equation. In the ¯rst place, we present a non-trivial sta- tionary solution wave. Then, we extract the main features of this solution to obtain a frontier condition between the initiation of the travelling waves and a decay to the resting state. This frontier corresponds to a separatrix in the projected dynamics diagram depending on the width and the amplitude of the stationary wave.

ANALYTICAL DETERMINATION OF INITIAL CONDITIONS LEADING TO FIRING IN NERVE FIBERS

2007

International audience; An analytical solution characterizing initial conditions leading to action potential firing in smooth nerve fibers is determined, using the bistable equation. In the first place, we present a nontrivial stationary solution wave, then, using the perturbative method, we analyze the stability of this stationary wave. We show that it corresponds to a frontier between the initiation of the travelling waves and a decay to the resting state. Eventually, this analytical approach is extended to FitzHugh-Nagumo model.