Transforming complex multistability to controlled monostability.

Multistability, a commonly observed feature among nonlinear systems, could be inconvenient under various circumstances. We demonstrate that a control in the form of slow and weak periodic parameter modulation can be effectively applied to transform a complex multistable system to a controlled monostable one. For the representative of a nonlinear system, we choose the Hénon map as the standard model. The number of coexisting stable states is known to increase as the dissipativity reduces. We show that even in the low dissipative limit, when the number of coexisting states could be arbitrarily large, the periodic parameter modulation can destroy the states coexisting with stable period 1. Thus, the system can be brought from any other branch to period-1 branch, leading to controlled monostability. This method works in the presence of noise as well.