Impulsive feedback control of birhythmicity: Theory and experiment

Area of Science:

• Nonlinear Dynamics
• Control Theory
• Systems Biology

Background:

• Birhythmicity, characterized by two distinct rhythms, is prevalent in biological and engineering systems.
• Controlling complex dynamic behaviors like birhythmicity is crucial for understanding and manipulating these systems.

Purpose of the Study:

• To develop and analyze an impulsive feedback control scheme for dynamic control of birhythmicity.
• To establish analytical conditions for effective birhythmicity control.
• To demonstrate the robustness and applicability of the proposed control scheme.

Main Methods:

• Impulsive feedback control strategy with ON/OFF switching.
• Harmonic decomposition and energy balance methods for analytical derivation.
• Numerical analysis in parameter space for efficacy assessment.
• Experimental validation in a birhythmic electronic circuit with noise.

Main Results:

• The system can be steered to any desired limit cycle of the original birhythmic oscillation by tuning feedback pulse parameters (height and width).
• Rigorous analytical conditions for controlling birhythmicity were derived.
• The control scheme demonstrated robustness against noise and parameter fluctuations.
• Successful application shown in energy harvesting, glycolysis, and p53-mdm2 networks.

Conclusions:

• Impulsive feedback control offers an effective and robust method for dynamic control of birhythmicity.
• The derived analytical conditions provide a theoretical foundation for practical implementation.
• The demonstrated applicability across diverse systems highlights the broad potential of this control strategy.