A generalized finite-time analytical approach for the synchronization of chaotic and hyperchaotic systems

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Muhammad Haris ◽  
Muhammad Shafiq ◽  
Adyda Ibrahim ◽  
Masnita Misiran
Keyword(s):  
Finite Time ◽  
Chaotic Systems ◽  
Closed Loop ◽  
Time Synchronization ◽  
Linear Part ◽  
Content Type ◽  
Nonlinear Part ◽  
Analytical Stability ◽  
Chaotic Signals ◽  
The Stability

PurposeThe purpose of this paper is to develop some interesting results in the field of chaotic synchronization with a new finite-time controller to reduce the time of convergence.Design/methodology/approachThis article proposes a finite-time controller for the synchronization of hyper(chaotic) systems in a given time. The chaotic systems are perturbed by the model uncertainties and external disturbances. The designed controller achieves finite-time synchronization convergence to the steady-state error without oscillation and elimination of the nonlinear terms from the closed-loop system. The finite-time synchronization convergence reduces the hacking duration and recovers the embedded message in chaotic signals within a given preassigned limited time. The free oscillation convergence keeps the energy consumption low and alleviates failure chances of the actuator. The proposed finite-time controller is a combination of linear and nonlinear parts. The linear part keeps the stability of the closed-loop, the nonlinear part increases the rate of convergence to the origin. A generalized form of analytical stability proof is derived for the synchronization of chaotic and hyper-chaotic systems. The simulation results provide the validation of the accomplish synchronization for the Lu chaotic and hyper-chaotic systems.FindingsThe designed controller not only reduces the time of convergence without oscillation of the trajectories which can run the system for a given time domain.Originality/valueThis work is originally written by the author.

Finite-time synchronization of delayed fractional-order quaternion-valued memristor-based neural networks

2020 ◽  
pp. 2150032
Author(s):  
Dawei Ding ◽  
Ziruo You ◽  
Yongbing Hu ◽  
Zongli Yang ◽  
Lianghui Ding
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Finite Time ◽  
Time Synchronization ◽  
Linear Part ◽  
State Feedback Control ◽  
Razumikhin Technique ◽  
Quaternion Multiplication ◽  
Control Schemes ◽  
The Stability

This paper mainly concerns with the finite-time synchronization of delayed fractional-order quaternion-valued memristor-based neural networks (FQVMNNs). First, the FQVMNNs are studied by separating the system into four real-valued parts owing to the noncommutativity of quaternion multiplication. Then, two state feedback control schemes, which include linear part and discontinuous part, are designed to guarantee that the synchronization of the studied networks can be achieved in finite time. Meanwhile, in terms of the stability theorem of delayed fractional-order systems, Razumikhin technique and comparison principle, some novel criteria are derived to confirm the synchronization of the studied models. Furthermore, two methods are used to obtain the estimation bounds of settling time. Finally, the feasiblity of the synchronization methods in quaternion domain is validated by the numerical examples.

scholarly journals Finite Time Synchronization for Fractional Order Sprott C Systems with Hidden Attractors

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Cui Yan ◽  
He Hongjun ◽  
Lu Chenhui ◽  
Sun Guan
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Engineering Practice ◽  
Fractional Order Systems ◽  
Spectral Entropy ◽  
Hidden Attractors ◽  
Finite Time Stability ◽  
Peculiar Phenomenon

Fractional order systems have a wider range of applications. Hidden attractors are a peculiar phenomenon in nonlinear systems. In this paper, we construct a fractional-order chaotic system with hidden attractors based on the Sprott C system. According to the Adomain decomposition method, we numerically simulate from several algorithms and study the dynamic characteristics of the system through bifurcation diagram, phase diagram, spectral entropy, and C0 complexity. The results of spectral entropy and C0 complexity simulations show that the system is highly complex. In order to apply such research results to engineering practice, for such fractional-order chaotic systems with hidden attractors, we design a controller to synchronize according to the finite-time stability theory. The simulation results show that the synchronization time is short and the robustness is stable. This paper lays the foundation for the study of fractional order systems with hidden attractors.

GLOBAL SYNCHRONIZATION OF A CLASS OF CHAOTIC SYSTEMS WITH A SCALAR TRANSMITTED SIGNAL

2004 ◽  
Vol 14 (04) ◽  
pp. 1431-1437 ◽  
Author(s):  
JUNGUO LU ◽  
YUGENG XI ◽  
XIAOFAN WANG
Keyword(s):  
Chaotic Systems ◽  
Linear Part ◽  
Feedback Gain ◽  
Chaotic Oscillator ◽  
Hyperchaotic System ◽  
State Variables ◽  
Error Feedback ◽  
Global Synchronization ◽  
Nonlinear Part ◽  
Output Error

This letter proposes a new global synchronization theorem for a class of chaotic systems. Specially, in the synchronization theorem neither the linear part nor the nonlinear part of the chaotic system requires the special structure indicated in [Wang & Wang, 1998]. We take a linear combination of the original system state variables as the scale-driving signal. We prove that the global synchronization can be attained through the simple linear output error feedback. The linear output error feedback gain is a function of a free parameter. We use Chua's chaotic oscillator and Saito's hyperchaotic system to illustrate the applicability of our synchronization scheme and discuss the issues concerning robustness.

Sign in / Sign up

Export Citation Format

Share Document