Imposing a Hopf bifurcation on a model estimated from noisy data from the delayed logistic equation

This paper solves the problem of identifying a nonlinear model from data produced by the delayed logistic equation with additive noise in such a way as to guarantee that the resulting model undergoes a Hopf bifurcation. The problem is solved by constrained optimization where the constraints guarantee the Hopf bifurcation at a given value of a generalized parameter, which is considered known a priori. The procedure is particularly interesting in the context of noisy data because under such circumstances it is known that the noise will shift the bifurcation points of the final model which can be corrected by the judicious use of prior knowledge.