Annihilation of One of the Coexisting Attractors in a Bistable System

A small change of one of the system parameters may not in general convert a bistable system to a monostable system. However, an external control in the form of a slow periodic parameter modulation can annihilate one of the coexisting states, and thus results in controlled monostability. The annihilation takes place because the state becomes chaotic via the period doubling route and the chaotic state undergoes boundary crisis within a small range of the control amplitude. These features are observed theoretically in two standard models, namely, Hénon map and laser rate equations, and confirmed experimentally in a cavity loss modulated CO₂ laser.