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## Phase portraits of random planar homogeneous vector fields

Author
Cima, A.; Gasull, A.; Mañosa, V.
Type of activity
Report
Date
2019-11-26
Code
arXiv:1911.11441 [math.DS]
Project funding
2017 SGR 388: Control, Modelitzacio´, Identificacio´ i Aplicacions (CoDAlab)
Rate-dependent hysteresis: modeling, analysis and identification, with applications to magnetorheological dampers
Repository
http://hdl.handle.net/2117/173969
URL
https://arxiv.org/abs/1911.11441
Abstract
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 problem and, moreover, either we give the exact value of each probability or we estimate it by using the Monte Carlo method. It is remarkable that all but two of these phase portraits are characterized by their index at the origin and by their number of invariant straight lines through it.
Citation
Cima, A.; Gasull, A.; Mañosa, V. "Phase portraits of random planar homogeneous vector fields". 2019.
Keywords
Index, Ordinary differential equations with random coefficients, Phase portraits, Planar homogeneous vector fields
Group of research
CoDAlab - Control, Dynamics and Applications