Seamless variation of isometric and anisometric dynamical integrity measures in basins's erosion

Anisometric integrity measures defined as improvement and generalization of two existing measures (LIM, local integrity measure, and IF, integrity factor) of the extent and compactness of basins of attraction are introduced. Non-equidistant measures make it possible to account for inhomogeneous sensitivities of the state space variables to perturbations, thus permitting a more confident and targeted identification of the safe regions. All four measures are used for a global dynamics analysis of the twin-well Duffing oscillator, which is performed by considering a nearly continuous variation of a governing control parameter, thanks to the use of parallel computation allowing reasonable CPU time. This improves literature results based on finite (and commonly large) variations of the parameter, due to computational constraints. The seamless evolution of key integrity measures highlights the fine aspects of the erosion of the safe domain with respect to the increasing forcing amplitude.