Robustness of cluster synchronous patterns in smallworld networks with intercluster cocompetition balance
Abstract
All edges in the classical Watts and Strogatz's smallworld network model are unweighted and cooperative (positive). By introducing competitive (negative) intercluster edges and assigning edge weights to mimic more realistic networks, this paper develops a modified model which possesses cocompetitive weighted couplings and cluster structures while maintaining the common smallworld network properties of small average shortest path lengths and large clustering coefficients. Based on theoretical analysis, it is proved that the new model with intercluster cocompetition balance has an important dynamical property of robust cluster synchronous pattern formation. More precisely, clusters will neither merge nor split regardless of adding or deleting nodes and edges, under the condition of intercluster cocompetition balance. Numerical simulations demonstrate the robustness of the model against the increase of the coupling strength and several topological variations.
 Authors:
 School of Science, Hangzhou Dianzi University, Hangzhou 310018 (China)
 School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004 (China)
 Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong (China)
 Publication Date:
 OSTI Identifier:
 22250672
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 24; Journal Issue: 2; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPUTERIZED SIMULATION; LENGTH; TOPOLOGY; VARIATIONS
Citation Formats
Zhang, Jianbao, Ma, Zhongjun, Email: mzj1234402@163.com, and Chen, Guanrong. Robustness of cluster synchronous patterns in smallworld networks with intercluster cocompetition balance. United States: N. p., 2014.
Web. doi:10.1063/1.4873524.
Zhang, Jianbao, Ma, Zhongjun, Email: mzj1234402@163.com, & Chen, Guanrong. Robustness of cluster synchronous patterns in smallworld networks with intercluster cocompetition balance. United States. doi:10.1063/1.4873524.
Zhang, Jianbao, Ma, Zhongjun, Email: mzj1234402@163.com, and Chen, Guanrong. Sun .
"Robustness of cluster synchronous patterns in smallworld networks with intercluster cocompetition balance". United States.
doi:10.1063/1.4873524.
@article{osti_22250672,
title = {Robustness of cluster synchronous patterns in smallworld networks with intercluster cocompetition balance},
author = {Zhang, Jianbao and Ma, Zhongjun, Email: mzj1234402@163.com and Chen, Guanrong},
abstractNote = {All edges in the classical Watts and Strogatz's smallworld network model are unweighted and cooperative (positive). By introducing competitive (negative) intercluster edges and assigning edge weights to mimic more realistic networks, this paper develops a modified model which possesses cocompetitive weighted couplings and cluster structures while maintaining the common smallworld network properties of small average shortest path lengths and large clustering coefficients. Based on theoretical analysis, it is proved that the new model with intercluster cocompetition balance has an important dynamical property of robust cluster synchronous pattern formation. More precisely, clusters will neither merge nor split regardless of adding or deleting nodes and edges, under the condition of intercluster cocompetition balance. Numerical simulations demonstrate the robustness of the model against the increase of the coupling strength and several topological variations.},
doi = {10.1063/1.4873524},
journal = {Chaos (Woodbury, N. Y.)},
number = 2,
volume = 24,
place = {United States},
year = {Sun Jun 15 00:00:00 EDT 2014},
month = {Sun Jun 15 00:00:00 EDT 2014}
}

Random Boolean Networks (RBNs) are often used as generic models for certain dynamics of complex systems, ranging from social networks, neural networks, to gene or protein interaction networks. Traditionally, RBNs are interconnected randomly and without considering any spatial arrangement of the links and nodes. However, most realworld networks are spatially extended and arranged with regular, smallworld, or other nonrandom connections. Here we explore the RBN network topology between extreme local connections, random smallworld, and random networks, and study the damage spreading with small perturbations. We find that spatially local connections change the scaling of the relevant component at very lowmore »

Damage Spreading in Spatial and Smallworld Random Boolean Networks
The study of the response of complex dynamical social, biological, or technological networks to external perturbations has numerous applications. Random Boolean Networks (RBNs) are commonly used a simple generic model for certain dynamics of complex systems. Traditionally, RBNs are interconnected randomly and without considering any spatial extension and arrangement of the links and nodes. However, most realworld networks are spatially extended and arranged with regular, powerlaw, smallworld, or other nonrandom connections. Here we explore the RBN network topology between extreme local connections, random smallworld, and pure random networks, and study the damage spreading with small perturbations. We find that spatially local connections change the scaling of the relevant component at very low connectivities (more » 
Dynamical meanfield approximation to smallworld networks of spiking neurons: From local to global and/or from regular to random couplings
By extending a dynamical meanfield approximation previously proposed by the author [H. Hasegawa, Phys. Rev. E 67, 041903 (2003)], we have developed a semianalytical theory which takes into account a wide range of couplings in a smallworld network. Our network consists of noisy Nunit FitzHughNagumo neurons with couplings whose average coordination number Z may change from local (Z<<N) to global couplings (Z=N1) and/or whose concentration of random couplings p is allowed to vary from regular (p=0) to completely random (p=1). We have taken into account three kinds of spatial correlations: the onsite correlation, the correlation for a coupled pair, andmore » 
Synchronizations in smallworld networks of spiking neurons: Diffusive versus sigmoid couplings
By using a semianalytical dynamical meanfield approximation previously proposed by the author [H. Hasegawa, Phys. Rev. E 70, 066107 (2004)], we have studied the synchronization of stochastic, smallworld (SW) networks of FitzHughNagumo neurons with diffusive couplings. The difference and similarity between results for diffusive and sigmoid couplings have been discussed. It has been shown that with introducing the weak heterogeneity to regular networks, the synchronization may be slightly increased for diffusive couplings, while it is decreased for sigmoid couplings. This increase in the synchronization for diffusive couplings is shown to be due to their local, negative feedback contributions, but notmore » 
Twodimensional smallworld networks: Navigation with local information
A navigation process is studied on a variant of the WattsStrogatz smallworld network model embedded on a square lattice. With probability p, each vertex sends out a longrange link, and the probability of the other end of this link falling on a vertex at lattice distance r away decays as r{sup {alpha}}. Vertices on the network have knowledge of only their nearest neighbors. In a navigation process, messages are forwarded to a designated target. For {alpha}<3 and {alpha}{ne}2, a scaling relation is found between the average actual path length and pL, where L is the average length of the additionalmore »