Periodic forces combined with feedback induce quenching in a bistable oscillator

Area of Science:

• Nonlinear dynamics
• Complex systems analysis
• Mathematical modeling

Background:

• Bistable oscillators exhibit both abnormal rhythms (limit cycles) and stable states (fixed points), mirroring natural phenomena like epilepsy.
• Understanding oscillation quenching, the transition from a limit cycle to a fixed point, is crucial but remains incompletely understood.

Purpose of the Study:

• To investigate the mechanism of oscillation quenching in a bistable system.
• To analyze the behavior of the extended Stuart-Landau oscillator under periodic forcing.
• To explore state-transition methods for controlling abnormal oscillations.

Main Methods:

• Utilized numerical simulations of the extended Stuart-Landau oscillator.
• Applied an averaging method to reduce the system's complexity.
• Investigated bifurcation structures under periodic forcing with quadratic feedback.

Main Results:

• Periodic forces can induce amplitude changes in the limit cycle through entrainment.
• Oscillation quenching was identified to occur via homoclinic bifurcation.
• Diverse bifurcation structures were revealed in periodically driven bistable oscillators.

Conclusions:

• Developed a state-transition method using periodic forces to control and quench abnormal oscillations in bistable systems.
• The findings contribute to a deeper understanding of complex behaviors in non-autonomous systems.
• Potential for practical applications in managing irregular rhythms and oscillations.