scholarly journals Adaptive Modified Function Projective Synchronization of Uncertain Complex Dynamical Networks with Multiple Time-Delay Couplings and Disturbances

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Jie Fang ◽  
Na Liu ◽  
Junwei Sun
Keyword(s):  
Time Delay ◽  
Sufficient Conditions ◽  
Dynamic Network ◽  
Projective Synchronization ◽  
Definite Function ◽  
Multiple Time ◽  
Complex Dynamic ◽  
Reference Node ◽  
Function Projective Synchronization ◽  
Modified Function Projective Synchronization

This paper studies the modified function projective synchronization of uncertain complex dynamic network model with multiple time-delay couplings and external disturbances. Based on Lyapunov stability theory, the positive definite function is designed and the sufficient conditions of synchronization are given. Both the uncertain parameters and the unknown bounded disturbances are estimated in accordance with the adaptive laws. With the adaptive feedback controller, the complex dynamic network can synchronize with reference node by a scaling function matrix. The reference node can be periodic orbit, equilibrium point, or a chaotic attractor. Finally, two numerical simulations are offered to illustrate the effectiveness of the proposed method.

scholarly journals Modified Function Projective Synchronization of Financial Hyperchaotic Systems via Adaptive Impulsive Controller with Unknown Parameters

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Guoliang Cai ◽  
Lingling Zhang ◽  
Lan Yao ◽  
Xiulei Fang
Keyword(s):  
Sufficient Conditions ◽  
Impulsive System ◽  
Stability Theorem ◽  
Projective Synchronization ◽  
Lyapunov Stability Theorem ◽  
Unknown Parameters ◽  
Function Projective Synchronization ◽  
Modified Function Projective Synchronization ◽  
The Stability ◽  
Hyperchaotic Systems

Modified function projective synchronization via adaptive impulsive controller between two different financial hyperchaotic systems is investigated, where the external uncertainties are considered. The updated laws of the unknown parameters are given and the sufficient conditions are deduced based on Lyapunov stability theorem and the stability analysis of impulsive system. Finally, the two financial hyperchaotic systems are taken for example and the numerical examples are worked through for illustrating the main results.

Modified function projective synchronization between two different complex networks with delayed couplings and delayed nodes of different dimensions

2016 ◽  
Vol 27 (11) ◽  
pp. 1650126 ◽  
Author(s):  
Min Han ◽  
Yamei Zhang ◽  
Meng Zhang
Keyword(s):  
Hybrid Control ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Linear Matrix ◽  
Function Projective Synchronization ◽  
Special Cases ◽  
Modified Function Projective Synchronization ◽  
Different Dimensions ◽  
Nodes Of Different Dimensions

In this paper, to deal with the problem of modified function projective synchronization (MFPS) between two different networks with delayed couplings and delayed nodes of different dimensions, a hybrid control scheme combining adaptive control and nonlinear control is proposed. First, a more realistic drive-response complex network model is constructed by introducing double delays. Then, we design hybrid feedback controllers to synchronize up the drive and response networks of different dimensions to a scaling function matrix. Based on Lyapunov stability theory and the linear matrix inequality (LMI), we rigorously prove that the MFPS between the proposed drive-response networks can be achieved and meanwhile some sufficient conditions are derived by adopting an appropriate Lyapunov–Krasovskii energy function. Noteably, many existing synchronization settings can be regarded as special cases of the present synchronization framework. Numerical simulation experiments are employed to verify the correctness and the effectiveness of the proposed method.

Exponential synchronization of a Markovian jump complex dynamic network with piecewise-constant transition rates and distributed delay

2018 ◽  
Vol 41 (9) ◽  
pp. 2535-2544 ◽  
Author(s):  
Nasim Akbari ◽  
Ali Sadr ◽  
Ali Kazemy
Keyword(s):  
Time Delay ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Dynamic Network ◽  
Exponential Synchronization ◽  
Linear Matrix ◽  
Transition Rates ◽  
Markovian Jump ◽  
Piecewise Constant ◽  
Time Varying Delay

The exponential synchronization of a Markovian jump complex dynamical network with piecewise-constant transition rates is investigated. Two distinct types of time-varying delay are considered for the system; one is distributed time-delay for each node, the other is discrete coupling time-delay. Based on an augmented Lyapunov–Krasovskii functional, some sufficient conditions are derived and expressed in the form of linear matrix inequalities, which are formulated in such a manner as to determine the controller gain matrices. Finally, an example is given to illustrate the effectiveness and validity of the proposed method.

scholarly journals Analysis and modified function projective synchronization of integer and fractional-order autonomous Morse jerk oscillator

2021 ◽  
Vol 5 (2) ◽  
pp. 275-280
Author(s):  
Dongmo ERİC DONALD ◽  
Cyrille AİNAMON ◽  
Alex Stéphane KEMNANG TSAFACK ◽  
Nasr SAEED ◽  
Victor KAMDOUM ◽  
...  
Keyword(s):  
Fractional Order ◽  
Projective Synchronization ◽  
Function Projective Synchronization ◽  
Modified Function Projective Synchronization

Generalized Hybrid Dislocated Function Projective Synchronization of Chaotic Systems with Time Delay

2014 ◽  
Vol 574 ◽  
pp. 672-678 ◽  
Author(s):  
Rui Li ◽  
Guang Jun Zhang ◽  
Tao Zhu ◽  
Xu Jing Wang ◽  
Jun Dong
Keyword(s):  
Time Delay ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Control Method ◽  
Scaling Factor ◽  
Projective Synchronization ◽  
Feedback Gain ◽  
Uncertain Parameters ◽  
Function Projective Synchronization ◽  
Feedback Control Method

In order to improve the security of secure communication, a novel generalized hybrid dislocated function projective synchronization (GHDFPS) was proposed and GHDFPS of time delay chaotic systems with uncertain parameters were researched in this paper. Due to time delay, the chaotic system can produce multiple positive Lyapunov exponential; this characteristic can enhance security in secure communications noticeably. Based on Lyapunove stability theory and modified hybrid feedback control method, the modified hybrid feedback controller and the parameter updating laws were designed for the GHDFPS between the two time delay chaotic systems with uncertain parameters. The feedback gain can be adjusted automatically according to the synchronization error values. Under the controller, generalized hybrid dislocated function projective synchronization of the two chaotic systems is achieved, and the uncertain parameters of response systems are identified. The chaotic item is added in the function scale factor. The chaotic item in the function scaling factor makes function scaling factor more complex and unpredictable. So this can enhance the features of indeterminism in secure communication. The time delay feedback Lorenz system as an example; by numerical simulations the effectiveness of the proposed method is demonstrated.

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