On connecting trajectories with maximum persistence of behavior

The problem of connecting two trajectories from a set with particular behavior is considered. The objective is to make such a transition inconspicuous in that the characteristic behaviors should persist during the transition. Such particular behaviors classes can be stationary solutions, limit cycles, or more general classes. The problem follows the abstract framework of Gluskabi raccordations given in. We first consider the raccordation problem without path constraints in two ways using different measures to quantify 'persistence of behavior'. We then generalize the framework to raccordations with dynamical constraints. For each case we consider the quasi-harmonic and the quasi-periodic transitions.