RT Journal Article
T1 Periodic orbits in hysteretic systems with real eigenvalues
A1 Esteban, Marina.
A1 Ponce, Enrique.
A1 Torres, Francisco.
K1 Discontinuous piecewise linear systems
K1 Liénard equation
K1 Limit cycles
AB Planar piecewise linear systems with hysteresis coming from a dimensional reduction in symmetric 3D systems with slow–fast dynamics are considered. We concentrate our attention on the cases of saddle and node dynamics, determining the existence and stability of periodic orbits as well as possible bifurcations. Our analysis rigorously shows, apart from standard bifurcations, as saddle-node bifurcation of periodic orbits and homoclinic and heteroclinic connections, the existence of specific grazing bifurcation. A pitchfork bifurcation of periodic orbits has been also detected, being responsible for the coexistence of up to four different periodic orbits. We illustrate the usefulness of the achieved theoretical results by justifying the appearance of periodic orbits in a concrete 3D system.
PB Springer
YR 2019
FD 2019-07-22
LK https://hdl.handle.net/10433/22274
UL https://hdl.handle.net/10433/22274
LA en
NO Esteban, M., Ponce, E. & Torres, F. Periodic orbits in hysteretic systems with real eigenvalues. Nonlinear Dyn 97, 2557–2578 (2019). https://doi.org/10.1007/s11071-019-05148-6
NO Departamento de Economía, Métodos Cuantitativos e Historia Económica. Universidad Pablo de Olavide.
DS RIO
RD May 9, 2026