Control of birhythmicity: A self-feedback approach

Area of Science:

• Complex Systems Dynamics
• Biophysics
• Systems Biology

Background:

• Birhythmicity, characterized by two distinct rhythms, is prevalent in various natural and artificial systems.
• Controlling birhythmicity is crucial for understanding and manipulating complex system behaviors.

Purpose of the Study:

• To propose and validate a general self-feedback scheme for controlling birhythmicity.
• To demonstrate the scheme's efficacy across diverse scientific domains.

Main Methods:

• Application of a self-feedback control scheme to three birhythmic oscillators.
• Utilizing harmonic decomposition and energy balance methods for analytical derivations.
• Performing numerical bifurcation analysis in parameter space.

Main Results:

• Analytical conditions for controlling birhythmicity were derived.
• The control scheme successfully eliminated birhythmicity in all tested models.
• The scheme induced transitions between different forms of bistability.

Conclusions:

• The proposed self-feedback scheme offers a general approach to control birhythmicity.
• This method has broad applicability in biochemical and engineering systems for managing complex dynamics.