Stable Degree Analysis for Profile of Networked Evolutionary Games With Disturbances

This paper studies the stable degree for profile of networked evolutionary games (NEGs) with disturbances by the semi-tensor product of matrices. Firstly, the algebraic formulation of an NEG with disturbances is established. Secondly, on the basis of algebraic formulation, some concepts about stable profile with disturbances are proposed, including strong k-degree stable and weak k-degree stable, and the corresponding criteria to detect the stable degree are presented. Thirdly, two algorithms for designing controls are given to make the stable profile achieves strong k-degree stable or weak k-degree stable. Finally, an example is given to illustrate the validity of the results.