Control of multistability in hidden attractors

Hidden attractors have a basin of attraction which is not connected with unstable equilibrium. Certain systems with hidden attractor show multistability for a range of parameter. Multistability or coexistence of different attractors in nonlinear systems often creates inconvenience and therefore, needs to be avoided to obtain a desired specific output from the system. We discuss the control of multistability in the hidden attractor through the scheme of linear augmentation, that can drive the multistable system to a monostable state. With the proper choice of control parameters a shift from multistability to monostability can be achieved. This transition from multiple attractors to a single attractor is confirmed by calculating the basin size as a measure. When a nonlinear system with hidden attractors is coupled with a linear system, two important transitions are observed with the increase of coupling strength: transition from multistability to monostability and then stabilization of newly created equilibrium point via suppression of oscillations.