Emmanuel Fleurantin

George Mason University | GMU · Department of Mathematical Sciences

We make a detailed numerical study of a three dimensional dissipative vector field derived from the normal form for a cusp-Hopf bifurcation. The vector field exhibits a Neimark–Sacker bifurcation giving rise to an attracting invariant torus. Our main goals are to (A) follow the torus via parameter continuation from its appearance to its disappearan...

The disparity in the impact of COVID-19 on minority populations in the United States has been well established in the available data on deaths, case counts, and adverse outcomes. However, critical metrics used by public health officials and epidemiologists, such as a time dependent viral reproductive number $ R_t $, can be hard to calculate from th...

Analyzing when noisy trajectories, in the two dimensional plane, of a stochastic dynamical system exit the basin of attraction of a fixed point is specifically challenging when a periodic orbit forms the boundary of the basin of attraction. Our contention is that there is a distinguished Most Probable Escape Path (MPEP) crossing the periodic orbit...

A bstract The COVID-19 pandemic has imposed many strenuous effects on the global economy, community, and medical infrastructure. Since the out- break, researchers and policymakers have scrambled to develop ways to identify how COVID-19 will affect specific sub-populations so that good public health decisions can be made. To this end, we adapt the w...

We make a detailed numerical study of the dynamics of a three dimensional dissipative vector field exhibiting a Neimark-Sacker bifurcation. Our main goals are to follow the attracting invariant torus born out of this bifurcation to its destruction in subsequent appearance of a chaotic attractor, and also to study the stable/unstable manifolds of th...

We make a detailed numerical study of the dynamics of a three dimensional dissipative vector field exhibiting a Neimark-Sacker bifurcation. Our main goals are to follow the attracting invariant torus born out of this bifurcation to its destruction in subsequent appearance of a chaotic attractor, and also to study the stable/unstable manifolds of th...

This work studies existence and regularity questions for attracting invariant tori in three dimensional dissipative systems of ordinary differential equations. Our main result is a constructive method of computer assisted proof which applies to explicit problems in non-perturbative regimes. We obtain verifiable bounds on the regularity of the attra...

Traditionally, the monolayer (two-dimensional) cell cultures are used for initial evaluation of the effectiveness of anticancer therapies. In particular, these experiments provide the IC50 curves that determine drug concentration that can inhibit growth of a tumor colony by half. The multicellular spheroid (three-dimensional) cultures have a histol...