Controlling birhythmicity in a new Dual Loop Optoelectronic Oscillator with an injection locked van der Pol oscillator

In the present literature, an attempt has been made to understand the birhythmic behaviour of a modified time delayed Dual Loop Optoelectronic Oscillator (DLOEO). To this end, an analytical solution of periodic oscillation is obtained using weakly nonlinear analysis. Two coexisting periodic oscillations are identified, considering shorter loop delay as a control parameter. Subsequently, to control the birhythmicity, a self-feedback mechanism is applied that incorporates the variable to be controlled and its canonical conjugate. Our study reveals that with proper control of the feedback strength, birhythmicity can be removed and monorhythmicity can be induced in the oscillator. •Birhythmicity is coexistence of two different limit cycle oscillations depending upon different initial conditions.•In the present work we analyse a modified Dual Loop OEO.•Using weakly nonlinear analysis the amplitude and phase equation of the oscillator is derived.•Due to the interplay between two delays and the overall nonlinearity birhythmicity emerges in the oscillator.•Subsequently a conjugate self feedback technique is applied to control the delay induced birhythmicity in the system.