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Necessary conditions for the controllability on linear systems with positive control are presented. The real case is analyzed and the Jordan form representation is employed. The minimum number of necessary controls to obtain controllability is remarked.
— In this paper we establish conditions to control the Hopf bifurcation of nonlinear systems with two uncontrollable modes on the imaginary axis. We use the center manifold to reduce the system dynamics to dimension two, and find expressions in terms of the original vector fields.