Strong resonances at Hopf bifurcations in control systems. (English. Russian original) Zbl 1093.34527
Autom. Remote Control 62, No. 11, 1783-1802 (2001); translation from Avtom. Telemekh. 2001, No. 11, 29-50 (2001).
Summary: The 0:1 and 1:1 resonances at Hopf bifurcations in control systems with a parameter are investigated. Conditions for the generation of cycles in the neighborhood of the equilibrium position and at infinity are formulated. Nonlinearities with a principle quadratic part and with a principle homogeneous part of the general (nonpolynomial) type in the neighborhood of the equilibrium position are separately studied. The main case of bounded saturation nonlinearities at infinity is also studied.
MSC:
| 34C23 | Bifurcation theory for ordinary differential equations |
| 34H05 | Control problems involving ordinary differential equations |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 37G15 | Bifurcations of limit cycles and periodic orbits in dynamical systems |
| 37N35 | Dynamical systems in control |
