Stability of the spreading in small-world network with predictive controller

Z J Bao; Q Y Jiang; W J Yan; Y J Cao

doi:10.1016/j.physleta.2010.01.045

Stability of the spreading in small-world network with predictive controller

Phys Lett A. 2010 Mar 29;374(13):1560-1564. doi: 10.1016/j.physleta.2010.01.045. Epub 2010 Jan 25.

Authors

Z J Bao¹, Q Y Jiang¹, W J Yan¹, Y J Cao^{1

2}

Affiliations

¹ College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China.
² College of Electrical and Information Engineering, Hunan University, Changsha 410082, China.

Abstract

In this Letter, we apply the predictive control strategy to suppress the propagation of diseases or viruses in small-world network. The stability of small-world spreading model with predictive controller is investigated. The sufficient and necessary stability condition is given, which is closely related to the controller parameters and small-world rewiring probability p. Our simulations discover a phenomenon that, with the fixed predictive controller parameters, the spreading dynamics become more and more stable when p decreases from a larger value to a smaller one, and the suitable controller parameters can effectively suppress the spreading behaviors even when p varies within the whole spectrum, and the unsuitable controller parameters can lead to oscillation when p lies within a certain range.

Keywords: Oscillation; Predictive control; Small-world network; Spreading; Stability.