Supplementary material
S. Zeng, “On sample-based computations of invariant sets,” to appear in Nonlinear Dynamics.
Preprint, SpringerLink
Computing the invariant set of the Van der Pol oscillator by employing the set-valued “trimming” iteration described in the paper:
The “trimming” iteration corresponds to a stable forward propagation of the original blue square under the dynamics of the Van der Pol system (an actual forward iteration of the blue set, which is described in terms of samples is bound to thin out in the middle due to the convergence to the limit cycle).
Computing the invariant set of the Hénon map with a=2.0 and b=0.3 using an efficient implementation by means of an adaptive regrowing-trimming iteration:
Download for the Matlab code for the Hénon example: