Stability and bifurcation of disease spreading in complex networks |
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| Authors: | Xiang Li Guanrong Chen Chunguang Li |
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| Affiliation: | 1. Department of Automation , Shanghai Jiaotong University , Shanghai, 200030, P. R. China;2. Department of Electronic Engineering , City University of Hong Kong , 83 Tat Chee Avenue, Kowloon, Hong Kong, P. R. China;3. Institute of Electronic Systems , College of Electronic Engineering, University of Electronic Science and Technology of China , Chengdu, Sichuan, 610054, P. R. China |
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| Abstract: | A general nonlinear model of disease spreading is proposed, describing the effect of the new link-adding probability p in the topological transition of the N-W small-world network model. The new nonlinear model covers both limiting cases of regular lattices and random networks, and presents a more flexible internal nonlinear interaction than a previous model. Hopf bifurcation is proved to exist during disease spreading in all typical cases of regular lattices, small-world networks, and random networks described by this model. It is shown that probability p not only determines the topological transition of the N-W small-world network model, but also dominates the stability of the local equilibria and bifurcating periodic solutions, and moreover can be further applied to stabilize a periodic spreading behaviour onto a stable equilibrium over the network. |
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