# A Memristor-Based Hyperchaotic Complex Lü System and Its Adaptive Complex Generalized Synchronization

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## Abstract

**:**

## 1. Introduction

## 2. A New MHCLS and Its Properties

#### 2.1. Generation of MHCLS

#### 2.2. Dissipation of MHCLS

#### 2.3. Symmetry and Invariance of MHCLS

#### 2.4. Equilibria and Stability of MHCLS

## 3. Dynamical Behaviors of MHCLS

#### 3.1. Hyperchaotic Behavior

#### 3.2. Chaotic Behavior

**Figure 5.**Transient behavior. (

**a**) Transient chaos to Period-5 (${a}_{2}=21.15$); (

**b**) Transient chaos to Period-3 orbit (${a}_{2}=30.19$).

#### 3.3. Periodic Behavior

#### 3.4. Transient Behavior

## 4. ACGS of Two Identical MHCLSs with Unknown Parameters

#### 4.1. Design of ACGS

**Definition 1.**

**Theorem 1.**

**Proof.**

#### 4.2. ACGS of Two Identical MHCLSs

#### 4.3. Numerical Simulations of ACGS

#### 4.4. The Application of ACGS to Secure Communication

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Wang, S.; Wang, X.; Zhou, Y.; Han, B.
A Memristor-Based Hyperchaotic Complex Lü System and Its Adaptive Complex Generalized Synchronization. *Entropy* **2016**, *18*, 58.
https://doi.org/10.3390/e18020058

**AMA Style**

Wang S, Wang X, Zhou Y, Han B.
A Memristor-Based Hyperchaotic Complex Lü System and Its Adaptive Complex Generalized Synchronization. *Entropy*. 2016; 18(2):58.
https://doi.org/10.3390/e18020058

**Chicago/Turabian Style**

Wang, Shibing, Xingyuan Wang, Yufei Zhou, and Bo Han.
2016. "A Memristor-Based Hyperchaotic Complex Lü System and Its Adaptive Complex Generalized Synchronization" *Entropy* 18, no. 2: 58.
https://doi.org/10.3390/e18020058