title: Robustness of cluster synchronous patterns in small-world networks with inter-cluster co-competition balance.
abstract: All edges in the classical Watts and Strogatz's small-world network model are unweighted and cooperative (positive). By introducing competitive (negative) inter-cluster edges and assigning edge weights to mimic more realistic networks, this paper develops a modified model which possesses co-competitive weighted couplings and cluster structures while maintaining the common small-world network properties of small average shortest path lengths and large clustering coefficients. Based on theoretical analysis, it is proved that the new model with inter-cluster co-competition 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 inter-cluster co-competition balance. Numerical simulations demonstrate the robustness of the model against the increase of the coupling strength and several topological variations.
authors.affiliation: School of Science, Hangzhou Dianzi University, Hangzhou 310018, China.
authors.forename: Jianbao
authors.initials: J
authors.lastname: Zhang
authors.affiliation: School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China.
authors.forename: Zhongjun
authors.initials: Z
authors.lastname: Ma
authors.affiliation: Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong, China.
authors.forename: Guanrong
authors.initials: G
authors.lastname: Chen