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8 papers
Persistence of periodic traveling waves and Abelian integrals
Armengol Gasull, Anna Geyer, Víctor Mañosa
It is well known that the existence of traveling wave solutions (TWS) for many partial differential equations (PDE) is a consequence of the fact that an associated planar ordinary…
A dynamic Parrondo's paradox for continuous seasonal systems
Anna Cima, Armengol Gasull, Víctor Mañosa
We show that planar continuous alternating systems, which can be used to model systems with seasonality, can exhibit a type of Parrondo's dynamic paradox, in which the stability of…
Phase portraits of random planar homogeneous vector fields
Anna Cima, Armengol Gasull, Víctor Mañosa
We study the phase portraits with positive probability of random planar homogeneous vector fields of degree n. In particular, for n=1,2,3, we give a complete solution of the proble…
Stability index of linear random dynamical systems
Anna Cima, Armengol Gasull, Víctor Mañosa
Given a homogeneous linear discrete or continuous dynamical system, its stability index is given by the dimension of the stable manifold of the zero solution. In particular, for th…
Minor loops of the Dahl and LuGre models
Fayçal Ikhouane, Víctor Mañosa, Gisela Pujol
Hysteresis is a special type of behavior encountered in physical systems: in a hysteretic system, when the input is periodic and varies slowly, the steady-state part of the output-…
Periodic orbits of discrete and continuous dynamical systems via Poincaré-Miranda theorem
Armengol Gasull, Víctor Mañosa
We present a systematic methodology to determine and locate analytically isolated periodic points of discrete and continuous dynamical systems with algebraic nature. We apply this…