scholarly journals Secure Complex Systems: A Dynamic Model in the Synchronization

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Abdulsattar Abdullah Hamad ◽  
M. Lellis Thivagar ◽  
Jalawi Alshudukhi ◽  
Talal Saad Alharbi ◽  
Saud Aljaloud ◽  
...  
Keyword(s):  
Nonlinear Control ◽  
Lyapunov Stability ◽  
Dynamic Systems ◽  
Stability Theory ◽  
Information Transfer ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Highly Nonlinear ◽  
System Synchronization ◽  
And Control

Chaotic systems are one of the most significant systems of the technological period because their qualities must be updated on a regular basis in order for the speed of security and information transfer to rise, as well as the system’s stability. The purpose of this research is to look at the special features of the nine-dimensional, difficult, and highly nonlinear hyperchaotic model, with a particular focus on synchronization. Furthermore, several criteria for such models have been examined; Hamiltonian, synchronizing, Lyapunov expansions, and stability are some of the terms used. The geometrical requirements, which play an important part in the analysis of dynamic systems, are also included in this research due to their importance. The synchronization and control of complicated networks’ most nonlinear control is important to use and is based on two major techniques. The linearization approach and the Lyapunov stability theory are the foundation for attaining system synchronization in these two ways.

Anti-Synchronization of Pan and Lorenz-Lu-Liu-Cai Chaotic Systems by Active Nonlinear Control

2012 ◽  
Vol 3 (2) ◽  
pp. 15-25 ◽  
Author(s):  
Ayub Khan ◽  
Ram Pravesh Prasad
Keyword(s):  
Nonlinear Control ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Exponential Synchronization ◽  
Global Exponential Synchronization

In this paper, the authors investigate the anti-synchronization of chaotic Pan, Lorenz, and Lu systems and anti-synchronization of Liu and Cai systems. Global exponential synchronization of Pan, Lorenz, Lu, Liu, and Cai chaotic systems are established by using Lyapunov stability theory. Numerical simulations are performed to illustrate the effectiveness of the proposed synchronization schemes for Pan, Lorenz, Lu, Liu, and Cai chaotic systems.

scholarly journals Anti-synchronization in different new chaotic systems via active nonlinear control

2013 ◽  
Vol 23 (2) ◽  
pp. 229-242
Author(s):  
Ayub Khan ◽  
Ram Pravesh Prasad
Keyword(s):  
Nonlinear Control ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory

In this paper, we discuss anti-synchronization between two identical new chaotic systems and anti-synchronization between another two identical new chaotic systems by active nonlinear control. The sufficient conditions for achieving the anti-synchronization of two new chaotic systems are derived based on Lyapunov stability theory. Numerical simulations are provided for illustration and verification of the proposed method.

scholarly journals Lyapunov stability theory for dynamic systems on time scales

1992 ◽  
Vol 5 (3) ◽  
pp. 275-281 ◽  
Author(s):  
Billur Kaymakçalan
Keyword(s):  
Time Scales ◽  
Lyapunov Stability ◽  
Comparison Principle ◽  
Dynamic Systems ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Existence Theory ◽  
Lyapunov’S Second Method ◽  
Stability Results

By use of the necessary calculus and the fundamental existence theory for dynamic systems on time scales, in this paper, we develop Lyapunov's second method in the framework of general comparison principle so that one can cover and include several stability results for both types of equations at the same time.

scholarly journals On Full-State Hybrid Projective Synchronization of General Discrete Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Adel Ouannas
Keyword(s):  
Lyapunov Stability ◽  
Discrete Time ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Full State ◽  
Hybrid Projective Synchronization ◽  
Nonlinear Control Method

The problems of full-state hybrid projective synchronization (FSHPS) and inverse full-state hybrid projective synchronization (IFSHPS) for general discrete chaotic systems are investigated in 2D. Based on nonlinear control method and Lyapunov stability theory, new controllers are designed to study FSHPS and IFSHPS, respectively, for 2D arbitrary chaotic systems in discrete-time. Numerical example and simulations are used to validate the main results of this paper.

scholarly journals Adaptive Terminal Synergetic Synchronization of Hyperchaotic Systems

2021 ◽  
Vol 54 (5) ◽  
pp. 789-795
Author(s):  
Yamina Haddadji ◽  
Mohamed Naguib Harmas ◽  
Abdlouahab Bouafia ◽  
Ziyad Bouchama
Keyword(s):  
Nonlinear Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Initial Conditions ◽  
Lyapunov Stability Theory ◽  
Slave System ◽  
Unknown Parameters ◽  
Master System ◽  
Simulation Results ◽  
Hyperchaotic Systems

This research paper introduces an adaptive terminal synergetic nonlinear control. This control aims at synchronizing two hyperchaotic Zhou systems. Thus, the adaptive terminal synergetic control’s synthesis is applied to synchronize a hyperchaotic i.e., slave system with unknown parameters with another hyperchaotic i.e., master system. Accordingly, simulation results of each system in different initial conditions reveal significant convergence. Moreover, the findings proved stability and robustness of the suggested scheme using Lyapunov stability theory.

scholarly journals The Synchronization of N Cascade-Coupled Chaotic Systems

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Pengyu Li ◽  
Juan Du ◽  
Shouliang Li ◽  
Yazhao Zheng ◽  
Bowen Jia
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
General Criterion ◽  
Synchronization Method ◽  
Bidirectional Coupling ◽  
Coupling Parameters

In this paper, we investigate a novel synchronization method, which consists of nn≥2 cascade-coupled chaotic systems. Furthermore, as the number of chaotic systems decreases from n to 2, the proposed synchronization will transform into bidirectional coupling synchronization. Based on Lyapunov stability theory, a general criterion is proposed for choosing the appropriate coupling parameters to ensure cascading synchronization. Moreover, 4 Lü systems are taken as an example and the corresponding numerical simulations demonstrate the effectiveness of our idea.

DIGITAL CRYPTOGRAPHY AND FEEDBACK SYNCHRONIZATION OF CHAOTIC SYSTEMS

2011 ◽  
Vol 25 (04) ◽  
pp. 521-529 ◽  
Author(s):  
MALA MITRA ◽  
SANTO BANERJEE
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Coupled System ◽  
Lyapunov Stability Theory ◽  
Chaotic Synchronization ◽  
Feedback Controller ◽  
New Method ◽  
Secure Communications

Secure communications via chaotic synchronization is demonstrated in this literature. At first we have designed a feedback controller for chaotic synchronization utilizing the Lyapunov stability theory for cascade-connected systems.The method has been applied successfully to make two identical systems globally asymptotically synchronized. The result of numerical simulations are given to validate the effectiveness of this method. Then we have discussed a new method of cryptography for this coupled system which is very simple to implement and effective.

scholarly journals Adaptive Synchronization of Chaotic SC-CNN with Uncertain State Template

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Phuong Dam Thanh ◽  
Cat Pham Thuong
Keyword(s):  
Neural Network ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Cellular Neural Network ◽  
Uncertain Parameter ◽  
Adaptive Synchronization ◽  
Chaotic State ◽  
Control Laws

The problem of synchronization of chaotic State Controlled Cellular Neural Network (SC-CNN) with uncertain state template is investigated. In detail, the following three cases are solved: firstly, synchronization of two identical chaotic SC-CNNs with uncertain state template, secondly, synchronization of two nonidentical chaotic SC-CNNs with all uncertain state templates, and, thirdly, synchronization between chaotic SC-CNN with uncertain state template and different uncertain parameter chaotic systems. The controllers and update laws proposed in each case are proved closely based on Lyapunov stability theory. In addition, some illustrative corresponding examples are presented to demonstrate the effectiveness and usefulness of the proposed control laws.

scholarly journals Effective Synchronization of a Class of Chua’s Chaotic Systems Using an Exponential Feedback Coupling

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Patrick Louodop ◽  
Hilaire Fotsin ◽  
Elie B. Megam Ngouonkadi ◽  
Samuel Bowong ◽  
Hilda A. Cerdeira
Keyword(s):  
Computer Simulations ◽  
Lyapunov Stability ◽  
Exponential Function ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Response Systems ◽  
The Stability ◽  
Systems Framework

A robust exponential function based controller is designed to synchronize effectively a given class of Chua's chaotic systems. The stability of the drive-response systems framework is proved through the Lyapunov stability theory. Computer simulations are given to illustrate and verify the method.

Dual Combination Synchronization of Six Chaotic Systems

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
Junwei Sun ◽  
Suxia Jiang ◽  
Guangzhao Cui ◽  
Yanfeng Wang
Keyword(s):  
Adaptive Control ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Combination Synchronization

Based on combination synchronization of three chaotic systems and combination–combination synchronization of four chaotic systems, a novel scheme of dual combination synchronization is investigated for six chaotic systems in the paper. Using combined adaptive control and Lyapunov stability theory of chaotic systems, some sufficient conditions are attained to realize dual combination synchronization of six chaotic systems. The corresponding theoretical proofs and numerical simulations are presented to demonstrate the effectiveness and correctness of the dual combination synchronization. Due to the complexity of dual combination synchronization, it will be more secure and interesting to transmit and receive signals in application of communication.

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