---
author:
- 'Simon Christ [^1]'
- Bernard Sonnenschein
- 'Lutz Schimansky-Geier'
bibliography:
- 'TwoState.bib'
date: 'Received: date / Revised version: date'
title: 'Tristable and multiple bistable activity in complex random binary networks of two-state units'
---

Introduction {#intro}
============

Discrete-state stochastic models can be used to describe discrete processes such as the orientation of a spin or the blinking of quantum dots [@Frantsuzov09]. Additionally, systems with continuously changing dynamics can be mapped to discrete-state descriptions via coarse-graining [@Lindner2004; @HuberTsim2005; @PikovskyTsim2001]. Despite the simplicity of the single units, the collective effects of ensembles of coupled units can be highly non-trivial.

In earlier works discrete stochastic three-state models have been used to investigate fluctuation driven spin nucleation on complex networks [@Chen15]. Two- and three-state models have been applied to neuronal systems [@Dumont2014; @PrFaSchiZa07] and recently to language dynamics [@Colaiori15]. Synchronization behavior, phase transitions and reaction to time delayed feedback [@WoodLind06; @WoodLind07; @WoodLind06PRE; @Prager2003; @EscaffLind12; @Kouvaris2010; @HuberTsim2005; @PikovskyTsim2001] as well as excitability [@Prager2007; @Leonhardt2008] are general aspects that apply to a wide range of natural phenomena.

Most of the referenced works consider Markovian – thereby memoryless – discrete-state models [@WoodLind06; @WoodLind07; @WoodLind06PRE; @Pinto2014]. A disordered environment [@Trimper04] or the reduction of models 