Multistability and its control in a simple chaotic circuit with a pair of light-emitting diodes
This paper investigates the multistability phenomenon and its control in a simple chaotic circuit with a pair of light emitting diodes proposed by Volos and collaborators (Nonlinear Dyn. 89:1047-1061, 2017). The bifurcation analysis reveals that chaos occurs in the circuit via period-doubling transition and symmetry-restoring crisis scenarios. In addition for a suitable parameters setting and different initial conditions, the circuit exhibits the coexistence of four disconnected periodic and chaotic attractors. This striking feature of the circuit is further characterized by computing the cross sections of the basin of attraction in which we define the set of initial conditions where each attractor can be found. Furthermore, due to the inconveniences of multistability behavior in many nonlinear systems, the control of this phenomenon is discussed by using the linear augmentation scheme. It is proved that by choosing the specific control parameters, the transition from multistable system to monostable system is achieved. Finally, an appropriate electronic circuit capable to emulate the dynamics of the system is designed and some analog simulations are point out to validate the numerical analysis.
CYBERNETICS AND PHYSICS, Vol. 6, No. 3. 2017, 114–120