Bifurcation Dynamics in Control Systems
نویسندگان
چکیده
This chapter deals with bifurcation dynamics in control systems, which are described by ordinary differential equations, partial differential equations and delayed differential equations. In particular, bifurcations related to double Hopf, combination of double zero and Hopf, and chaos are studied in detail. Center manifold theory and normal form theory are applied to simplify the analysis. Explicit stability conditions are derived and routes of bifurcations leading to various complex dynamics are given. A system with time delayed feedback control is studied to show that time delay plays a important role in controlling and anti-controlling chaotic motions. Furthermore, a simple feedback controller is designed for anti-controlling Hopf bifurcation arising in the Lorenz system.
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