Control of Dynamic Hopf Bifurcations
Berglund, Nils
HAL, hal-00130547 / Harvested from HAL
Text on HAL
The slow passage through a Hopf bifurcation leads to the delayed appearance of large amplitude oscillations. We construct a smooth scalar feedback control which suppresses the delay and causes the system to follow a stable equilibrium branch. This feature can be used to detect in time the loss of stability of an ageing device. As a by-product, we obtain results on the slow passage through a bifurcation with double zero eigenvalue, described by a singularly perturbed cubic Lienard equation.
Publié le : 2000-07-05
Classification:  Hopf bifurcation,  nonlinear control theory,  singular perturbations,  dynamic bifurcations,  codimension four unfolding,  Liénard equation,  MSC 34E15, 58F14, 93D15,  [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC],  [NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD] 
@article{hal-00130547,
     author = {Berglund, Nils},
     title = {Control of Dynamic Hopf Bifurcations},
     journal = {HAL},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00130547}
}

Berglund, Nils. Control of Dynamic Hopf Bifurcations. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-00130547/