A special type of explosion of basin boundary

Abstract

We study a special type of explosion of a basin boundary set in an archetypal oscillator. A typical feature is that the basin boundaries change the number of basins separating at the same time. Before the explosion, a basin boundary contains some Wada points of ten basins. After the explosion, the basin boundary contains some Wada points of eighteen basins. The underlying mechanism for the explosion is investigated by the heteroclinic tangency and Lambda lemma. Basin entropy and boundary basin entropy are also used to describe the nature of basins of attraction and the basin boundary explosion.