Symmetric piecewise linear bi-dimensional systems are very common in control engineering. They constitute a class of non-differentiable vector fields for which classical Hopf bifurcation theorems are not applicable. For such systems, sufficient and necessary conditions for bifurcation of a limit cycle from the periodic orbit at infinity are given.
@article{urn:eudml:doc:41281,
title = {Hoptf bifurcation from infinity for planar control systems.},
journal = {Publicacions Matem\`atiques},
volume = {41},
year = {1997},
pages = {181-198},
mrnumber = {MR1461650},
zbl = {0883.34043},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41281}
}
Llibre, Jaume; Ponce, Enrique. Hoptf bifurcation from infinity for planar control systems.. Publicacions Matemàtiques, Tome 41 (1997) pp. 181-198. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41281/