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Bifurcation Tailoring via Newton Flow-Aided Adaptive Control

The aim of bifurcation tailoring is to design an appropriate control law such that the controlled system has a desired bifurcation diagram. After describing two open-loop bifurcation tailoring techniques, this paper proposes a new open-loop plus close-loop bifurcation tailoring method based on a combination of the Newton-flow algorithm and the minimal control synthesis (MCS) adaptive control strategy. This method is applied to the Duffing system as an illustrative example.