RT Journal Article
T1 A direct transition to chaos in hysteretic systems with focus dynamics
A1 Esteban, Marina
A1 Ponce, Enrique
A1 Torres, Francisco
K1 Dynamical Systems
K1 Hysteresis
K1 Chaos
AB A specific transition to chaos is detected in the study of periodic orbits of hysteretic systems with symmetry and dynamics of focus type. The corresponding bifurcation is rigorously justified by resorting to the analysis of transition maps, whose mathematical expressions are adequately derived. It is shown that, depending on a parameter related to the location of equilibria, such transition maps can pass from being a smooth function to a discontinuous, piecewise-smooth function. We deal with the intermediate situation for which the transition map is continuous but nonsmooth. Using a second parameter, and previous known results on chaotic maps, we show in a rigorous way the existence of a chaos boundary crisis bifurcation, where the transition from a configuration without periodic orbits to another with bounded chaotic solutions occurs.
PB AIP Publishing
YR 2019
FD 2019-10-08
LK https://hdl.handle.net/10433/22275
UL https://hdl.handle.net/10433/22275
LA en
NO Chaos 29, 103111 (2019)
NO Departamento de Economía, Métodos Cuantitativos e Historia Económica. Universidad Pablo de Olavide.
DS RIO
RD May 9, 2026