FERNÁNDEZ GARCÍA , Soledad

This year is the 100th anniversary of the death of Jules Henri Poincaré (Nancy, France, 29 April 1854-Paris, France, 17 July 1912), the founding father of Dynamical Systems theory. In mathematics, he is known as The Last Universalist, since he excelled in all fields of the discipline during his life. As it is well-known, the motivation of part...

Tras haber superado una serie de dificultades de diversos tipos, entre ellas de género, de carácter y de enfermedad, la norteamericana Nancy Kopell ha llegado a ser una de la biomatemáticas más reconocidas en la actualidad por sus excelentes contribuciones en el avance de la neurociencia, al estudiar a partir de los sistemas dinámicos las...

In this article, we prove the existence of a saddle-node bifurcation of limit cycles in continuous piecewise linear systems with three zones. The bifurcation arises from the perturbation of a non-generic situation, where there exists a linear center in the middle zone. We obtain an approximation of the relation between the parameters of the...

In this work we deal with the canard regime as a part of a canard explosion taking place in a PWL version of the van der Pol equation having a flat critical manifold. The proposed analysis involves the identification of two specific canard cycles, one at the beginning and the other at the end of the canard regime, here called birth and...

In this work, we introduce an iterative optimization algorithm to obtain the intrinsic Proper Generalized Decomposition modes of elliptic partial differential equations. The main idea behind this procedure is to adapt the general Gradient Descent algorithm to the algebraic version of the intrinsic Proper Generalized Decomposition framework, and...

We study saddle-node bifurcations of canard limit cycles in PWL systems by using singular perturbation theory tools. We distinguish two cases: the subcritical and the supercritical. In the subcritical case, we find saddle-node bifurcations of canard cycles both with head and without head. Moreover, we detect a transition between them. In the...

By applying a singular perturbation approach, canard explosions exhibited by a general family of singularly perturbed planar Piecewise Linear (PWL) differential systems are analyzed. The performed study involves both hyperbolic and non-hyperbolic canard limit cycles appearing after both, a supercritical and a subcritical Hopf bifurcation. The...