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On creation of Hopf bifurcations in discrete-time nonlinear systems. (English) Zbl 1080.37567
Summary: Bifurcation characteristics of a nonlinear system can be manipulated by small controls. We present a control method to create Hopf bifurcations in discrete-time nonlinear systems. The critical conditions for the Hopf bifurcations are discussed. The center manifold method, normal form technique and the Iooss’s Hopf bifurcation theory are employed in the derivation of the control gain. Numerical demonstration is provided.
MSC:
37G15Bifurcations of limit cycles and periodic orbits