Bifurcation analysis, chaos and control in the Burgers mapping. (English) Zbl 1394.37123
Summary: The bifurcation analysis for a Burgers mapping is studied. The existence and stability of the fixed points of this map are derived. Conditions of existence for pitchfork bifurcation, flip bifurcation and Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. The control of the map around stable Neimark-Sacker bifurcation is achieved by using the feedback polynomial controller technique. The complex dynamics, bifurcations and chaos are displayed by numerical simulations.
MSC:
37N35 | Dynamical systems in control |
37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
39A10 | Additive difference equations |
39A12 | Discrete version of topics in analysis |