Self-organized stochastic tipping in slow-fast dynamical systems

TL;DR

This paper investigates how a neuron model adaptively achieves a target firing rate distribution, revealing spontaneous oscillations driven by noise, interpreted as self-organized stochastic tipping in slow-fast dynamical systems.

Contribution

It introduces a model of a neuron adapting its parameters to reach a target distribution, demonstrating spontaneous oscillations as a novel self-organized stochastic tipping phenomenon.

Findings

Spontaneous quasi-periodic oscillations occur during adaptation.

Noise induces transitions between quasi-stationary attractors.

Adaptive behavior results in self-organized stochastic tipping.

Abstract

Polyhomeostatic adaption occurs when evolving systems try to achieve a target distribution function for certain dynamical parameters, a generalization of the notion of homeostasis. Here we consider a single rate encoding leaky integrator neuron model driven by white noise, adapting slowly its internal parameters, the threshold and the gain, in order to achieve a given target distribution for its time-average firing rate. For the case of sparse encoding, when the target firing-rated distribution is bimodal, we observe the occurrence of spontaneous quasi-periodic adaptive oscillations resulting from fast transition between two quasi-stationary attractors. We interpret this behavior as self-organized stochastic tipping, with noise driving the escape from the quasi-stationary attractors.