Study on Congestion and Bursting in Small-World Networks with Time Delay from the Viewpoint of Nonlinear Dynamics

2012 ◽  
Vol 29 (6) ◽  
pp. 060504 ◽  
Author(s):  
Yan Liu ◽  
Li-Guang Liu ◽  
Hang Wang
Keyword(s):  
Nonlinear Dynamics ◽  
Time Delay ◽  
Small World ◽  
Small World Networks

SYNCHRONIZATION OF TIME DELAY FITZHUGH–NAGUMO SMALL-WORLD NETWORKS

2009 ◽  
Vol 20 (10) ◽  
pp. 1521-1529 ◽  
Author(s):  
YAN-LONG LI ◽  
JUN MA ◽  
YAN-JUN LIU ◽  
LI-PING ZHANG ◽  
JUN-YAN SU
Keyword(s):  
Time Delay ◽  
Order Parameter ◽  
Noise Intensity ◽  
Small World ◽  
Small World Networks ◽  
Wide Range ◽  
Excitable Systems ◽  
And Control ◽  
Range Of Values

The order parameters and synchronization are numerically investigated in the time delay small-world connected FitzHugh–Nagumo excitable systems. The simulations show that the order parameter continuously decreases with increasing D, the quality of the synchronization worsens for large noise intensity. As the coupling intensity goes up, the quality of the synchronization worsens also, and find that the larger rewiring probability becomes, the larger-order parameter. At the same time, the order parameter goes up, the time delay declines. We obtained the complete phase diagram for a wide range of values of noise intensity D and control parameter g.

Networks

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Complex Systems ◽  
Complex Networks ◽  
Phase Diagrams ◽  
Community Detection ◽  
Network Science ◽  
Small World ◽  
Small World Networks ◽  
Multilayer Networks ◽  
Basic Vocabulary

Understanding the interactions between the components of a system is key to understanding it. In complex systems, interactions are usually not uniform, not isotropic and not homogeneous: each interaction can be specific between elements.Networks are a tool for keeping track of who is interacting with whom, at what strength, when, and in what way. Networks are essential for understanding of the co-evolution and phase diagrams of complex systems. Here we provide a self-contained introduction to the field of network science. We introduce ways of representing and handle networks mathematically and introduce the basic vocabulary and definitions. The notions of random- and complex networks are reviewed as well as the notions of small world networks, simple preferentially grown networks, community detection, and generalized multilayer networks.

scholarly journals Multifractal analysis of eigenvectors of small-world networks

2021 ◽  
Vol 144 ◽  
pp. 110745
Author(s):  
Ankit Mishra ◽  
Jayendra N. Bandyopadhyay ◽  
Sarika Jalan
Keyword(s):  
Multifractal Analysis ◽  
Small World ◽  
Small World Networks
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