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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 wepresent a constructive method to produce dissipative dynamics which lead tostable periodic orbits as time grows, with predesigned transient dynamics.Depending on the construction method a) the limiting orbit can be a regularcircle, an ellipse or a more complex closed orbit and b) the approach to thelimiting orbit can follow an exponential law or a power law. This techniqueallows to design nonlinear models of dynamical systems with desired(exponential or power law) relaxation properties.

Constructive approach to limiting periodic orbits with exponential and power law dynamics