PWL approximation of dynamical systems: an example

The piecewise-linear approximation technique developed by Julian et al. (1999-2002) is applied to dynamical systems dependent on given numbers of state variables and parameters. Referring to a particular example, i.e., the two-dimensional Bautin equation, it is shown that an accurately approximated dynamical system preserves both the dynamical (trajectories) and the structural-stability (bifurcations) arrangements of the original system. In particular, if the approximation accuracy increases, the equivalence between approximating and approximated systems shifts from qualitative to quantitative.