CONSTRUCTING HOMOCLINIC ORBITS AND CHAOTIC ATTRACTORS

Homoclinic orbits and chaotic attractors are constructed progressively by singular perturbations. More specifically, lower dimensional slow subsystems and fast subsystems are constructed separately as building blocks. The former are than modulated onto the latter via homotopy. This gives a systematic way to implement Rossler's dual principle for mathematical modeling. Systems constructed in this way are simple, robust, and ideal for the purposes of experimental and theoretical analyses.