Signal-Coupled Subthreshold Hopf-Type Systems Show a Sharpened Collective Response

Area of Science:

• Dynamical Systems Theory
• Mathematical Biology
• Auditory Neuroscience

Background:

• Biological sensors often display remarkable properties explainable by dynamical systems near bifurcations.
• A Hopf bifurcation model successfully describes mammalian hearing across various scales, from hair bundles to cochlear regions.
• Scale invariance is a key observed property in biological sensory systems.

Purpose of the Study:

• To elucidate the underlying mechanism of scale invariance in biological sensors.
• To generalize findings beyond auditory systems to other dynamics near a Hopf bifurcation.
• To investigate the collective behavior of coupled systems below the bifurcation threshold.

Main Methods:

• Analysis of dynamical systems in the vicinity of a Hopf bifurcation.
• Modeling of ensembles of Hopf systems subjected to natural signal coupling.
• Comparison of collective bifurcation properties with individual system behaviors.

Main Results:

• Ensembles of coupled Hopf systems exhibit a collective Hopf bifurcation at parameters significantly below individual system thresholds.
• This collective bifurcation demonstrates scale invariance, explaining observed properties in biological sensors.
• The frequency profile of the collective bifurcation is sharpened compared to individual systems.

Conclusions:

• Signal coupling in ensembles of Hopf systems generates a collective bifurcation, explaining scale invariance in biological sensors.
• This collective behavior provides a generalizable framework applicable to various systems, including neuronal dynamics.
• The findings offer insights into efficient signal processing and emergent properties in biological systems.