# Synchronization of Butterfly Fractional Order Chaotic System

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## Abstract

**:**

## 1. Introduction

## 2. Main Results

**Lemma**

**1.**

**Proof.**

**Definition**

**1.**

**Definition**

**2.**

**Theorem**

**1.**

**Proof.**

**Remark**

**1.**

**Remark**

**2.**

**Remark**

**3.**

## 3. Examples

**Example**

**1.**

**Example**

**2.**

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Time response of the states ${u}_{1}\left(t\right),{u}_{2}\left(t\right),{u}_{3}\left(t\right)$ of the drive system (13) with fractional order $q=0.828$.

**Figure 2.**Time response of the states ${u}_{1}\left(t\right),{u}_{2}\left(t\right),{u}_{3}\left(t\right)$ of the drive system (13) with fractional order $q=0.9$.

**Figure 3.**Time response of the states ${u}_{1}\left(t\right),{u}_{2}\left(t\right),{u}_{3}\left(t\right)$ of the drive system (13) with fractional order $q=0.95$.

**Figure 4.**Time response of the states ${u}_{1}\left(t\right),{u}_{2}\left(t\right),{u}_{3}\left(t\right)$ of the drive system (13) with fractional order $q=0.99$.

**Figure 8.**Three-dimensional phase diagram of the states ${u}_{1}\left(t\right),{u}_{2}\left(t\right),{u}_{3}\left(t\right)$ of the drive system (13) with fractional order $q=0.9$.

**Figure 15.**Time response of the states ${e}_{1}\left(t\right),{e}_{2}\left(t\right),{e}_{3}\left(t\right)$ for the error system (15) with fractional order $q=0.9$.

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Fečkan, M.; Sathiyaraj, T.; Wang, J.
Synchronization of Butterfly Fractional Order Chaotic System. *Mathematics* **2020**, *8*, 446.
https://doi.org/10.3390/math8030446

**AMA Style**

Fečkan M, Sathiyaraj T, Wang J.
Synchronization of Butterfly Fractional Order Chaotic System. *Mathematics*. 2020; 8(3):446.
https://doi.org/10.3390/math8030446

**Chicago/Turabian Style**

Fečkan, Michal, T. Sathiyaraj, and JinRong Wang.
2020. "Synchronization of Butterfly Fractional Order Chaotic System" *Mathematics* 8, no. 3: 446.
https://doi.org/10.3390/math8030446