  In dynamical systems limit cycles arise as a result of a Hopf bifurcation,
after a control parameter has crossed its critical value. In this study we
present a constructive method to produce dissipative dynamics which lead to
stable periodic orbits as time grows, with predesigned transient dynamics.
Depending on the construction method a) the limiting orbit can be a regular
circle, an ellipse or a more complex closed orbit and b) the approach to the
limiting orbit can follow an exponential law or a power law. This technique
allows to design nonlinear models of dynamical systems with desired
(exponential or power law) relaxation properties.
