Stabilization of steady state in Multiplex heterogeneous networks of neuron-like models with bistability between silent state and bursting attractor

TL;DR

This paper investigates how multiplex heterogeneous networks of neuron-like models with bistability can be stabilized in a steady state through active communication, even with minimal defective elements.

Contribution

It introduces a multiplex network model with neuron-like oscillators exhibiting bistability and demonstrates stabilization of steady state via communication with defective channels.

Findings

Active communication in multiplex networks stabilizes steady states.

A single defective element can influence the entire network's stability.

Bistability arises from ion channel properties with non-monotonic characteristics.

Abstract

The dynamics of a multiplex heterogeneous network of oscillators is studied. Two types of similar models based on the Hodgkin-Huxley formalism are used as the basic elements of the networks. The first type model demonstrates bursting oscillations. The second model demonstrates bistability between bursting attractor and stable steady state. Basin of attraction of the stable equilibrium in the model is very small. Bistabilty is a result taking into account an additional ion channel, which has a non-monotonic characteristic and can be interpreted as a channel with a communication defect. Suggested multiplex networks assumed more active communication between models with a defect as a result in such networks it is enough to have one element with a communication defect in the subnetworks in order to stabilize the state of equilibrium in the entire network.