Space-dependent intermittent feedback can control birhythmicity.

Area of Science:

• Nonlinear Dynamics
• Complex Systems
• Control Theory

Background:

• Birhythmicity, characterized by two distinct rhythms, is observed in various physical and biological nonlinear systems.
• While essential for environmental adaptation in some biological systems, birhythmicity can reduce efficiency in physical systems, necessitating effective control strategies.

Purpose of the Study:

• To propose and validate a novel space-dependent intermittent control scheme for managing birhythmicity in diverse dynamical systems.
• To demonstrate the general applicability and efficiency of the proposed control method across different scientific domains.

Main Methods:

• Development of a space-dependent intermittent control scheme.
• Application and testing of the scheme on five distinct nonlinear systems.
• Analytical derivation of control conditions using harmonic decomposition and energy balance in a van der Pol oscillator.
• Numerical and bifurcation analyses to assess efficacy across a broad parameter space.

Main Results:

• The proposed control scheme successfully controlled birhythmic oscillations in all five tested nonlinear systems.
• Analytical conditions for controlling birhythmicity were derived for the van der Pol oscillator.
• The control scheme demonstrated efficiency and generality in managing complex dynamical behaviors.

Conclusions:

• The developed space-dependent intermittent control scheme is a general and efficient method for controlling birhythmicity.
• This approach holds potential for application in a wide range of physical and biological systems exhibiting complex oscillatory dynamics.