# Stability of Replicator Dynamics with Bounded Continuously Distributed Time Delay

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Replicator Dynamics with Bounded Continuously Distributed Delays

#### 2.1. The Mathematical Model

**Definition**

**1.**

**Remark**

**1.**

#### 2.2. Stability Analysis-Special Case

**Lemma**

**1.**

**Theorem**

**1.**

**Proof.**

#### 2.3. Stability Analysis-General Case

**Theorem**

**2.**

**Proof.**

**Theorem**

**3.**

**Proof.**

**Remark**

**2.**

## 3. Numerical Example

**Remark**

**3.**

#### 3.1. Special Case

#### 3.2. General Case

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**MDPI and ACS Style**

Zhong, C.; Yang, H.; Liu, Z.; Wu, J.
Stability of Replicator Dynamics with Bounded Continuously Distributed Time Delay. *Mathematics* **2020**, *8*, 431.
https://doi.org/10.3390/math8030431

**AMA Style**

Zhong C, Yang H, Liu Z, Wu J.
Stability of Replicator Dynamics with Bounded Continuously Distributed Time Delay. *Mathematics*. 2020; 8(3):431.
https://doi.org/10.3390/math8030431

**Chicago/Turabian Style**

Zhong, Chongyi, Hui Yang, Zixin Liu, and Juanyong Wu.
2020. "Stability of Replicator Dynamics with Bounded Continuously Distributed Time Delay" *Mathematics* 8, no. 3: 431.
https://doi.org/10.3390/math8030431