# Applications of the Network Simulation Method to Differential Equations with Singularities and Chaotic Behaviour

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## Abstract

**:**

## 1. Introduction

- Select the equivalence between physical and electrical variables;
- Apply the initial and boundary conditions using the appropriate electrical devices.

## 2. Methodology

## 3. Examples of Applications of NSM

#### 3.1. A Family of Differential Equations

**Theorem**

**1.**

**Proof.**

**Proposition**

**1.**

#### 3.2. Solution of Differential Equation of a Parabolic Mirror

#### 3.3. Van der Pol Equation

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 9.**Zoom of the Figure 5 with Matlab code.

**Figure 10.**Zoom of the Figure 6 with NSM.

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**MDPI and ACS Style**

Solano, J.; Balibrea, F.; Moreno, J.A.
Applications of the Network Simulation Method to Differential Equations with Singularities and Chaotic Behaviour. *Mathematics* **2021**, *9*, 1442.
https://doi.org/10.3390/math9121442

**AMA Style**

Solano J, Balibrea F, Moreno JA.
Applications of the Network Simulation Method to Differential Equations with Singularities and Chaotic Behaviour. *Mathematics*. 2021; 9(12):1442.
https://doi.org/10.3390/math9121442

**Chicago/Turabian Style**

Solano, Joaquín, Francisco Balibrea, and José Andrés Moreno.
2021. "Applications of the Network Simulation Method to Differential Equations with Singularities and Chaotic Behaviour" *Mathematics* 9, no. 12: 1442.
https://doi.org/10.3390/math9121442