Francisco A. Carrillo

ANALYSIS OF THE TAKENS-BOGDANOV BIFURCATION ON m-PARAMETERIZED VECTOR FIELDS

Given an m-parameterized family of n-dimensional vector fields, such that: (i) for some value of the parameters, the family has an equilibrium point, (ii) its linearization has a double zero eigenvalue and no other eigenvalue on the imaginary axis, sufficient conditions on the vector field are given such that the dynamics on the two-dimensional center manifold is locally topologically equivalent to the versal deformation of the planar Takens–Bogdanov bifurcation.

TRAVELING WAVES, CATASTROPHES AND BIFURCATIONS IN A GENERIC SECOND ORDER TRAFFIC FLOW MODEL

We consider the macroscopic, second order model of Kerner–Konhauser for traffic flow given by a system of PDE. Assuming conservation of cars, traveling waves solution of the PDE are reduced to a dynamical system in the plane. We prove that under generic conditions on the so-called fundamental diagram, the surface of critical points has a fold or cusp catastrophe and each fold point gives rise to a Takens–Bogdanov bifurcation. In particular, limit cycles arising from a Hopf bifurcation give place to traveling wave solutions of the PDE.

Takens‐Bogdanov Bifurcation Analysis in Indirect Field‐oriented Control

The influence of the normalized load and the rotor time constant mismatch on the dynamical behavior of induction motors under indirect field oriented control (IFOC) is analyzed. We focus the analysis on the Takens‐Bogdanov bifurcation using a recent generalization of the Takens‐Bogdanov bifurcation Theorem. We have found a criterion that allows us to determine which IFOC systems do not undergo such bifurcation.

ON CONTROLLABILITY OF LINEAR SYSTEMS WITH POSITIVE CONTROL

Abstract Necessary conditions for the controllability on linear systems with positive control are presented. The real case is analyzed and the Jordan form representation is employed. The minimum number of necessary controls to obtain controllability is remarked.

Global product structure for a space of special matrices

The importance of the Hurwitz–Metzler matrices and the Hurwitz symmetric matrices can be appreciated in different applications: communication networks, biology and economics are some of them. In this paper, we use an approach of differential topology for studying such matrices. Our results are as follows: the space of the

Control of the Planar Takens–Bogdanov Bifurcation with Applications

n\times n

Robust stabilization of positive linear systems via sliding positive control

n×n Hurwitz symmetric matrices has a product manifold structure given by the space of the