CHAOS GENERATION FOR A CLASS OF NONLINEAR COMPLEX NETWORKS

2013 ◽  
Vol 23 (02) ◽  
pp. 1350018 ◽  
Author(s):  
NA LIU ◽  
JUAN LI ◽  
ZHI-HONG GUAN ◽  
LI DING ◽  
GUILIN ZHENG
Keyword(s):  
Lyapunov Exponent ◽  
Complex Networks ◽  
Mathematical Analysis ◽  
Research Topic ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Numerical Example ◽  
Emergence Of Chaos ◽  
New Criteria ◽  
Theoretical Results

Chaos generation is an interesting research topic in the study of coupled complex dynamical networks. In this paper, based on mathematical analysis of Lyapunov exponent and boundedness of networks, the emergence of chaos for a class of nonlinear complex networks is investigated and some new criteria of chaos generation are derived. The effectiveness of theoretical results is verified by a numerical example.

Cluster Mixed Synchronization of Complex Networks with Disturbance

2015 ◽  
Vol 719-720 ◽  
pp. 448-451
Author(s):  
Li Jie Zeng
Keyword(s):  
Community Structure ◽  
Complex Networks ◽  
Numerical Simulations ◽  
Network Model ◽  
Complex Dynamical Networks ◽  
Time Varying ◽  
Dynamical Networks ◽  
Bounded Disturbances ◽  
Synchronization Scheme ◽  
Theoretical Results

In this paper, we investigate the cluster mixed synchronization scheme in time-varying delays coupled complex dynamical networks with disturbance. Basing on the community structure of the networks, some sufficient criteria are derived to ensure cluster mixed synchronization of the network model. Particularly, unknown bounded disturbances can be conquered by the proposed control. The numerical simulations are performed to verify the effectiveness of the theoretical results

scholarly journals Cluster Anti-Synchronization of Complex Networks with Nonidentical Dynamical Nodes

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Shuguo Wang ◽  
Chunyuan He ◽  
Hongxing Yao
Keyword(s):  
Community Structure ◽  
Complex Networks ◽  
Numerical Simulations ◽  
Network Model ◽  
Complex Dynamical Networks ◽  
Time Varying ◽  
Dynamical Networks ◽  
Nonidentical Nodes ◽  
Theoretical Results

This paper investigates a new cluster antisynchronization scheme in the time-varying delays coupled complex dynamical networks with nonidentical nodes. Based on the community structure of the networks, the controllers are designed differently between the nodes in one community that have direct connections to the nodes in other communities and the nodes without direct connections with the nodes in other communities strategy; some sufficient criteria are derived to ensure cluster anti-synchronization of the network model. Particularly, the weight configuration matrix is not assumed to be irreducible. The numerical simulations are performed to verify the effectiveness of the theoretical results.

scholarly journals Cluster Synchronization of Time-Varying Delays Coupled Complex Networks with Nonidentical Dynamical Nodes

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Shuguo Wang ◽  
Hongxing Yao ◽  
Mingping Sun
Keyword(s):  
Community Structure ◽  
Complex Networks ◽  
Numerical Simulations ◽  
Network Model ◽  
Complex Dynamical Networks ◽  
Cluster Synchronization ◽  
Time Varying ◽  
Dynamical Networks ◽  
Synchronization Scheme ◽  
Theoretical Results

This paper investigates a new cluster synchronization scheme in the nonlinear coupled complex dynamical networks with nonidentical nodes. The controllers are designed based on the community structure of the networks; some sufficient criteria are derived to ensure cluster synchronization of the network model. Particularly, the weight configuration matrix is not assumed to be symmetric, irreducible. The numerical simulations are performed to verify the effectiveness of the theoretical results.

STABILITY OF TWO TYPICAL COMPLEX DYNAMICAL NETWORKS

2008 ◽  
Vol 22 (05) ◽  
pp. 553-560 ◽  
Author(s):  
WU-JIE YUAN ◽  
XIAO-SHU LUO ◽  
PIN-QUN JIANG ◽  
BING-HONG WANG ◽  
JIN-QING FANG
Keyword(s):  
Numerical Simulation ◽  
Dissipative System ◽  
Small World ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
General Complex ◽  
The Stability ◽  
Theoretical Results

When being constructed, complex dynamical networks can lose stability in the sense of Lyapunov (i. s. L.) due to positive feedback. Thus, there is much important worthiness in the theory and applications of complex dynamical networks to study the stability. In this paper, according to dissipative system criteria, we give the stability condition in general complex dynamical networks, especially, in NW small-world and BA scale-free networks. The results of theoretical analysis and numerical simulation show that the stability i. s. L. depends on the maximal connectivity of the network. Finally, we show a numerical example to verify our theoretical results.

scholarly journals Pinning Synchronization of Switched Complex Dynamical Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Liming Du ◽  
Feng Qiao ◽  
Fengying Wang
Keyword(s):  
Lyapunov Function ◽  
Complex Networks ◽  
Function Method ◽  
Complex Dynamical Networks ◽  
Switching Topology ◽  
Dynamical Networks ◽  
Switching Law ◽  
Arbitrary Switching ◽  
Lyapunov Function Method ◽  
Networks With Switching Topology

Network topology and node dynamics play a key role in forming synchronization of complex networks. Unfortunately there is no effective synchronization criterion for pinning synchronization of complex dynamical networks with switching topology. In this paper, pinning synchronization of complex dynamical networks with switching topology is studied. Two basic problems are considered: one is pinning synchronization of switched complex networks under arbitrary switching; the other is pinning synchronization of switched complex networks by design of switching when synchronization cannot achieved by using any individual connection topology alone. For the two problems, common Lyapunov function method and single Lyapunov function method are used respectively, some global synchronization criteria are proposed and the designed switching law is given. Finally, simulation results verify the validity of the results.

scholarly journals H∞-Based Pinning Synchronization of General Complex Dynamical Networks with Coupling Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Bowen Du ◽  
Dianfu Ma
Keyword(s):  
Complex Dynamical Networks ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Feedback Controllers ◽  
External Disturbances ◽  
Dynamical Networks ◽  
Attenuation Index ◽  
General Complex ◽  
Local Feedback ◽  
Theoretical Results

This paper investigates the synchronization of complex dynamical networks with coupling delays and external disturbances by applying local feedback injections to a small fraction of nodes in the whole network. Based onH∞control theory, some delay-independent and -dependent synchronization criteria with a prescribedH∞disturbances attenuation index are derived for such controlled networks in terms of linear matrix inequalities (LMIs), which guarantee that by placing a small number of feedback controllers on some nodes, the whole network can be pinned to reach network synchronization. A simulation example is included to validate the theoretical results.

SYNCHRONIZATION INSIDE COMPLEX DYNAMICAL NETWORKS WITH DOUBLE TIME-DELAYS AND NONLINEAR INNER-COUPLING FUNCTIONS

2011 ◽  
Vol 25 (11) ◽  
pp. 1531-1541 ◽  
Author(s):  
WEIGANG SUN ◽  
YUEYING YANG ◽  
CHANGPIN LI ◽  
ZENGRONG LIU
Keyword(s):  
Vector Field ◽  
Complex Networks ◽  
Time Delays ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Numerical Examples ◽  
Theoretical Criterion ◽  
Double Time

In this article, synchronization inside complex networks with double time-delays and nonlinear inner-coupling functions are studied. Here double time-delays mean that each node vector field and every coupling node have retard time, while nonlinear inner-coupling functions refer to all the components of every node that are nonlinearly coupled. The theoretical criterion respecting synchronization is derived. And illustrative numerical examples are also given.

scholarly journals On the effects of memory and topology on the controllability of complex dynamical networks

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Panagiotis Kyriakis ◽  
Sérgio Pequito ◽  
Paul Bogdan
Keyword(s):  
Complex Networks ◽  
Temporal Dynamics ◽  
Complex Dynamical Networks ◽  
Long Term Memory ◽  
Topological Properties ◽  
Control Effort ◽  
Dynamical Networks ◽  
Term Memory ◽  
Minimum Number

Abstract Recent advances in network science, control theory, and fractional calculus provide us with mathematical tools necessary for modeling and controlling complex dynamical networks (CDNs) that exhibit long-term memory. Selecting the minimum number of driven nodes such that the network is steered to a prescribed state is a key problem to guarantee that complex networks have a desirable behavior. Therefore, in this paper, we study the effects of long-term memory and of the topological properties on the minimum number of driven nodes and the required control energy. To this end, we introduce Gramian-based methods for optimal driven node selection for complex dynamical networks with long-term memory and by leveraging the structure of the cost function, we design a greedy algorithm to obtain near-optimal approximations in a computationally efficiently manner. We investigate how the memory and topological properties influence the control effort by considering Erdős–Rényi, Barabási–Albert and Watts–Strogatz networks whose temporal dynamics follow a fractional order state equation. We provide evidence that scale-free and small-world networks are easier to control in terms of both the number of required actuators and the average control energy. Additionally, we show how our method could be applied to control complex networks originating from the human brain and we discover that certain brain cortex regions have a stronger impact on the controllability of network than others.

scholarly journals Pinning Two Nonlinearly Coupled Complex Networks with an Asymmetrical Coupling Matrix

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jianwen Feng ◽  
Ze Tang ◽  
Jingyi Wang ◽  
Yi Zhao
Keyword(s):  
Complex Networks ◽  
Lyapunov Stability Theory ◽  
Pinning Control ◽  
Feedback Controllers ◽  
Dynamical Networks ◽  
Synchronization Problem ◽  
Response Network ◽  
Control Schemes ◽  
Hybrid Synchronization ◽  
Theoretical Results

This paper addresses the hybrid synchronization problem in two nonlinearly coupled complex networks with asymmetrical coupling matrices under pinning control schemes. The hybrid synchronization of two complex networks is the outer antisynchronization between the driving network and the response network while the inner complete synchronization in the driving network and the response network. We will show that only a small number of pinning feedback controllers acting on some nodes are effective for synchronization control of the mentioned dynamical networks. Based on Lyapunov Stability Theory, some simple criteria for hybrid synchronization are derived for such dynamical networks by pinning control strategy. Numerical examples are provided to illustrate the effectiveness of our theoretical results.

Synchronization control of complex dynamical networks with piecewise constant arguments

2018 ◽  
Vol 41 (2) ◽  
pp. 540-551 ◽  
Author(s):  
Tianhu Yu ◽  
Menglong Su
Keyword(s):  
Impulsive Control ◽  
Lyapunov Stability Theory ◽  
Pinning Control ◽  
Complex Dynamical Networks ◽  
Control Law ◽  
Dynamical Networks ◽  
Piecewise Constant Arguments ◽  
Piecewise Constant ◽  
Synchronization Problem ◽  
Theoretical Results

The pinning synchronization problem is investigated for complex dynamical networks with hybrid coupling via impulsive control. Based on the Lyapunov stability theory, some novel synchronization criteria are derived and an impulsive pinning control law is proposed. By introducing a differential inequality for systems with piecewise constant arguments, it is not necessary to establish any relationship between the norms of the error states with or without piecewise constant arguments. Typical numerical examples are utilized to illustrate the validity and improvements as regards conservativeness of the theoretical results.

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