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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
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