# Emergence of Subcritical Bifurcations in a System of Randomly Coupled Supercritical Andronov-Hopf Oscillators: A Potential Mechanism for Neural Network Type Switching

## TL;DR

This paper introduces a model of coupled oscillators that can switch between different dynamic states, potentially explaining how neural networks adapt their processing modes in response to behavioral and stimulus changes.

## Contribution

It demonstrates that a system of supercritical oscillators can exhibit subcritical bifurcations, offering a new mechanism for neural network state switching.

## Key findings

- System exhibits both supercritical and subcritical bifurcations.
- Potential mechanism for neural network type switching.
- Model explains adaptive processing in cortical circuits.

## Abstract

Experimental evidence suggests that the computational state of cortical systems change according to behavioral and stimulus context. However, it is still unknown what mechanisms underlie this adaptive processing in cortical circuitry. In this paper, we present a model of randomly coupled supercritical Andronov-Hopf oscillators which can act as an adaptive processor by exhibiting drastically different dynamics depending on the value of a single network parameter. Despite being only composed of supercritical subunits, the full system can exhibit either supercritical or subcritical Andronov-Hopf bifurcations. This model might provide a novel mechanism for switching between globally asymptotically stable and nonhyperbolic neural network types in pattern recognition theory.