Synchronization in complex dynamical networks coupled with complex chaotic system

2015 ◽  
Vol 26 (06) ◽  
pp. 1550060 ◽  
Author(s):  
Qiang Wei ◽  
Cheng-Jun Xie ◽  
Bo Wang
Keyword(s):  
Chaotic System ◽  
Scaling Function ◽  
Complex Function ◽  
Complex Dynamical Networks ◽  
Real Field ◽  
Complex State ◽  
Dynamical Networks ◽  
State Variable ◽  
System A ◽  
Complex Chaotic System

This paper investigates synchronization in complex dynamical networks with time delay and perturbation. The node of complex dynamical networks is composed of complex chaotic system. A complex feedback controller is designed to realize different component of complex state variable synchronize up to different scaling complex function when complex dynamical networks realize synchronization. The synchronization scaling function is changed from real field to complex field. Synchronization in complex dynamical networks with constant delay and time-varying coupling delay are investigated, respectively. Numerical simulations show the effectiveness of the proposed method.

A New Type of Function Projective Synchronization of Nonautonomous Chaotic System

2013 ◽  
Vol 705 ◽  
pp. 590-595
Author(s):  
Xiao Shan Zhao ◽  
Zhen Bo Li ◽  
Fang Fang Liu
Keyword(s):  
Numerical Simulation ◽  
Chaotic System ◽  
Scaling Function ◽  
Projective Synchronization ◽  
Function Projective Synchronization ◽  
State Variable ◽  
Gyroscope System ◽  
New Type ◽  
The Scaling Function ◽  
General Method

The function projective synchronization of nonautonomous chaotic system with a new type of scaling function is investigated. The scaling function factor discussed in this paper is a new kind of function which contains the state variable. Obviously, this kind of scaling function is complicated than former ones. Based on modified active control, the general method of this synchronization is proposed. In numerical simulation, the heavy symmetric gyroscope system is taken as the instance to demonstrate the validity of the controller and the feasibility of the proposed synchronization.

Adaptive control of structural balance for complex dynamical networks based on dynamic coupling of nodes

2018 ◽  
Vol 32 (04) ◽  
pp. 1850042 ◽  
Author(s):  
Zilin Gao ◽  
Yinhe Wang ◽  
Lili Zhang
Keyword(s):  
Large Scale ◽  
The State ◽  
Point Of View ◽  
Complex Dynamical Networks ◽  
Relationship Matrix ◽  
Dynamical Networks ◽  
Structural Balance ◽  
Practical Applications ◽  
System A ◽  
The Social

In the existing research results of the complex dynamical networks controlled, the controllers are mainly used to guarantee the synchronization or stabilization of the nodes’ state, and the terms coupled with connection relationships may affect the behaviors of nodes, this obviously ignores the dynamic common behavior of the connection relationships between the nodes. In fact, from the point of view of large-scale system, a complex dynamical network can be regarded to be composed of two time-varying dynamic subsystems, which can be called the nodes subsystem and the connection relationships subsystem, respectively. Similar to the synchronization or stabilization of the nodes subsystem, some characteristic phenomena can be also emerged in the connection relationships subsystem. For example, the structural balance in the social networks and the synaptic facilitation in the biological neural networks. This paper focuses on the structural balance in dynamic complex networks. Generally speaking, the state of the connection relationships subsystem is difficult to be measured accurately in practical applications, and thus it is not easy to implant the controller directly into the connection relationships subsystem. It is noted that the nodes subsystem and the relationships subsystem are mutually coupled, which implies that the state of the connection relationships subsystem can be affected by the controllable state of nodes subsystem. Inspired by this observation, by using the structural balance theory of triad, the controller with the parameter adaptive law is proposed for the nodes subsystem in this paper, which may ensure the connection relationship matrix to approximate a given structural balance matrix in the sense of the uniformly ultimately bounded (UUB). That is, the structural balance may be obtained by employing the controlling state of the nodes subsystem. Finally, the simulations are used to show the validity of the method in this paper.

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