Adaptive Complex Function Projective Synchronization of Uncertain Complex Chaotic Systems

2015 ◽  
Vol 11 (1) ◽  
Author(s):  
Fangfang Zhang ◽  
Shutang Liu
Keyword(s):  
Real World ◽  
Chaotic Systems ◽  
Complex Function ◽  
Projective Synchronization ◽  
Real Field ◽  
Complex Field ◽  
Unknown Parameters ◽  
Function Projective Synchronization ◽  
Complex Chaotic Systems ◽  
Speed Gradient

Complex function projective synchronization (CFPS) is the most general synchronization and it enhances the security of communication. However, there always exist unknown parameters for chaotic systems in the real world. Considering all possible cases of unknown parameters of two complex chaotic systems, we design adaptive CFPS schemes and parameters update laws based on speed-gradient (SG) method. The convergence factors and pseudogradient condition are added to regulate the convergence speed and increase robustness. SG method is extended from real field to complex field. Numerical simulations are performed to demonstrate the effectiveness and feasibility of the proposed schemes.

FUNCTION PROJECTIVE SYNCHRONIZATION OF THE CHAOTIC SYSTEMS WITH PARAMETERS UNKNOWN

2013 ◽  
Vol 27 (21) ◽  
pp. 1350110
Author(s):  
JIAKUN ZHAO ◽  
YING WU
Keyword(s):  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Hyperchaotic System ◽  
Unknown Parameters ◽  
Function Projective Synchronization ◽  
Parameter Update Law ◽  
Different Chaotic Systems ◽  
Hyperchaotic Systems ◽  
Adaptive Control Law

This work is concerned with the general methods for the function projective synchronization (FPS) of chaotic (or hyperchaotic) systems. The aim is to investigate the FPS of different chaotic (hyper-chaotic) systems with unknown parameters. The adaptive control law and the parameter update law are derived to make the states of two different chaotic systems asymptotically synchronized up to a desired scaling function by Lyapunov stability theory. The general approach for FPS of Chen hyperchaotic system and Lü system is provided. Numerical simulations are also presented to verify the effectiveness of the proposed scheme.

Adaptive Modified Hybrid Robust Projective Synchronization Between Identical and Nonidentical Fractional-Order Complex Chaotic Systems With Fully Unknown Parameters

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Hadi Delavari ◽  
Milad Mohadeszadeh
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Order Complex ◽  
Unknown Parameters ◽  
Adaptive Sliding Mode Controller ◽  
Robust Adaptive ◽  
Complex Chaotic Systems

In this paper, a robust adaptive sliding mode controller is proposed. Under the existence of external disturbances, modified hybrid projective synchronization (MHPS) between two identical and two nonidentical fractional-order complex chaotic systems is achieved. It is shown that the response system could be synchronized with the drive system up to a nondiagonal scaling matrix. An adaptive controller and parameter update laws are investigated based on the Lyapunov stability theorem. The closed-loop stability conditions are derived based on the fractional-order Lyapunov function and Mittag-Leffler function. Finally, numerical simulations are given to verify the theoretical analysis.

scholarly journals Modified Function Projective Synchronization of Fractional Order Chaotic Systems with Different Dimensions

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hong-Juan Liu ◽  
Zhi-Liang Zhu ◽  
Hai Yu ◽  
Qian Zhu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Hyperchaotic System ◽  
Unknown Parameters ◽  
Adaptive Controllers ◽  
Function Projective Synchronization ◽  
Modified Function Projective Synchronization ◽  
Different Dimensions ◽  
The Stability

The modified function projective synchronization of different dimensional fractional-order chaotic systems with known or unknown parameters is investigated in this paper. Based on the stability theorem of linear fractional-order systems, the adaptive controllers with corresponding parameter update laws for achieving the synchronization are given. The fractional-order chaotic system and hyperchaotic system are applied to achieve synchronization in both reduced order and increased order. The corresponding numerical results coincide with theoretical analysis.

‎S‎ynchronization ‎of‎ different ‎dimensions‎ ‎fractional-‎order chaotic ‎systems with uncertain‎‎ ‎ parameters ‎and ‎secure ‎communication‎‎‎‎‎

2021 ◽  
Vol 39 (5) ◽  
pp. 57-72
Author(s):  
Vajiheh Vafaei ◽  
Hossein Kheiri ◽  
Aliasghar Jodayree Akbarfam
Keyword(s):  
Fractional Order ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Security Analysis ◽  
High Sensitivity ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Function Projective Synchronization ◽  
Fractional Order Controller

In ‎this ‎paper, ‎an‎ adaptive ‎modified‎ function projective synchronization (‎AM‎FPS) ‎scheme‎ ‎of ‎different ‎dimensions‎‎ ‎fractional-‎order ‎chaotic systems with ‎fully ‎unknown parameters is ‎presented‎. ‎On the basis of ‎fractional‎ Lyapunov stability ‎theory ‎and adaptive control law‎,‎ a‎ ‎new‎ fractional-order controller ‎and‎ suitable ‎‎‎‎update ‎rules‎ for unknown parameters are ‎designed‎‎ to realize the ‎AMFPS‎ of different ‎fractional-‎order chaotic systems with ‎non-‎identical ‎orders ‎and different dimensions‎‎. ‎‎Theoretical analysis and numerical simulations are given to verify the validity ‎of ‎the proposed ‎method. ‎Additionally, ‎‎‎‎synchronization results ‎are applied to secure communication via ‎‎ ‎modified ‎‎‎‎masking ‎method. Due to the unpredictability of the scale ‎function ‎matrix‎ and ‎using‎ of ‎fractional-‎order ‎systems with different ‎dimensions ‎and ‎u‎nequal‎ ‎orders,‎‎ the proposed scheme has higher ‎security‎‎. The security analysis ‎‎‎demonstrate that the proposed algorithm ‎has ‎a large key space ‎and‎ high sensitivity to encryption keys ‎and it is ‎‎re‎sistance to all kind of ‎‎attacks‎.

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