# Flows of Substances in Networks and Network Channels: Selected Results and Applications

## Abstract

**:**

## 1. Short Overview of Selected Areas of Research on Flows in Networks

## 2. Models of Network Flows Containing Differential Equations

## 3. Differential and Difference Equations for Modeling Flows in Channels of Networks: Selected Results

#### 3.1. Flow of a Substance in a Channel Constructed from Arms with an Infinite Number of Nodes Each

#### 3.2. Model of a Flow in a Channel of a Network Based on Difference Equations

**Theorem**

**1.**

**Theorem**

**2.**

## 4. Connection between the Theory of Flows in Networks and the Theory of Growth of Random Networks

## 5. Concluding Remarks

## Funding

## Institutional Review Board Statement

## Conflicts of Interest

## References

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**Figure 1.**The network and the channel. Solid lines denote nodes and edges that belong to the channel. Dashed lines denote the other nodes and edges of the network.

**Figure 2.**Numbering of the nodes of the channel. The lower two indexes of the numbers of the nodes are shown.

**Figure 3.**Flows connected with the i-th node of the channel. Nodes 0 and N exchange substances with only one of the other nodes of the channel. There is a possibility for an exchange of substances among flows between the nodes and (i) the network (arrows with dashed lines) or (ii) the environment of the network (arrows with dot-dashed lines).

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Dimitrova, Z.I.
Flows of Substances in Networks and Network Channels: Selected Results and Applications. *Entropy* **2022**, *24*, 1485.
https://doi.org/10.3390/e24101485

**AMA Style**

Dimitrova ZI.
Flows of Substances in Networks and Network Channels: Selected Results and Applications. *Entropy*. 2022; 24(10):1485.
https://doi.org/10.3390/e24101485

**Chicago/Turabian Style**

Dimitrova, Zlatinka I.
2022. "Flows of Substances in Networks and Network Channels: Selected Results and Applications" *Entropy* 24, no. 10: 1485.
https://doi.org/10.3390/e24101485