# Reaction Networks as a Language for Systemic Modeling: Fundamentals and Examples

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## Abstract

**:**

## 1. Introduction

## 2. Reaction Networks

#### 2.1. Relational Descriptions

**Definition**

**1.**

**Lemma**

**1.**

**Definition**

**2.**

**Definition**

**3.**

#### 2.2. Stoichiometric Description

**Definition**

**4.**

**Lemma**

**2.**

**Definition**

**5.**

**Definition**

**6.**

**Lemma**

**3.**

#### 2.3. Kinetic Description

## 3. Connecting the Description Levels: Chemical Organization Theory

**Definition**

**7.**

**Definition**

**8.**

**abstraction**of $\mathbf{x}\left(t\right)$. For a given set of species $X\subseteq \mathcal{M}$, a state $\mathbf{x}\left(t\right)\in {\mathbb{R}}_{\ge 0}^{m}$ is an

**instance**of X if and only if its abstraction equals X.

## 4. Discussion: Reaction Networks and the Modeling of Systems

#### 4.1. Reaction Networks as Universes and Organizations as Systems

#### 4.2. Inner and External Contexts

#### 4.3. The Emergence of Systems and Meta-Systems

#### 4.4. The Lack of Identity Problem and the Membrane Solution

#### 4.5. Resilience and Other Modern Systemic Notions

## 5. Examples

#### 5.1. Social System: Political Structure

#### 5.2. Decision System: Evolutionary Game Theory

#### 5.3. Ecological Systems

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Example of hierarchy of reaction networks and their properties in COT. Inspired from [14].

**Figure 2.**(

**a**) Topology of the reaction network model of the political system. Labelled boxes represent species and arrows represent reactions. (

**b**) The hierarchy of organizations.

**Figure 3.**Paradigm change from agent-based (

**bottom**) to reaction network (

**top**) modeling. The interaction among agents corresponds to a vessel of decision species interacting, and the payoff matrix corresponds to a set of reactions which consumes a pair of decisions to produce the payoff of each decision and two new decisions determined by the strategies.

**Table 1.**Table of scalability of properties depending on the level of representation. Each property is either not computable, or a level or scalability is associated. A property is more scalable if it can be computed for larger networks. Hence, Full, Moderate, and Hard scalability represent three levels of increasingly more complex computation, respectively.

Property-Type/Level | Relational | Stoichiometric | Kinetic |
---|---|---|---|

Topological Structure | Full | Full | Full |

Phase Space Analysis | Uncomputable | Moderate | Hard |

Time Evolution | Uncomputable | Moderate | Hard |

Reaction | Ecological Interaction |
---|---|

$prey+predator\to 2predator$ | Depredation |

$host+hosted\to 2hosted$ | Parasitism |

$host+hosted\to host+2hosted$ | Comensalism |

$host+hosted\to host$ | Amensalism |

${Coop}_{1}+{Coop}_{2}\to 2{Coop}_{1}+2{Coop}_{2}$ | Mutualism |

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Veloz, T.; Razeto-Barry, P.
Reaction Networks as a Language for Systemic Modeling: Fundamentals and Examples. *Systems* **2017**, *5*, 11.
https://doi.org/10.3390/systems5010011

**AMA Style**

Veloz T, Razeto-Barry P.
Reaction Networks as a Language for Systemic Modeling: Fundamentals and Examples. *Systems*. 2017; 5(1):11.
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**Chicago/Turabian Style**

Veloz, Tomas, and Pablo Razeto-Barry.
2017. "Reaction Networks as a Language for Systemic Modeling: Fundamentals and Examples" *Systems* 5, no. 1: 11.
https://doi.org/10.3390/systems5010011