Synchronization of switched networked evolutionary games
This paper investigates the synchronization problem of networked evolutionary games(NEGs)with switched networked structures.Firstly,the algebraic expression of the strategy profile dynamics is given by using the semi-tensor product(STP)of matrices,and a necessary and sufficient algebraic condition is presented to verify whether a switched NEG is synchronized to a static NEG.Then by constructing an auxiliary system and using the invariant subset-based method,the synchronization problem of switched NEGs can be converted into set stability of the auxiliary system with respect to a given nonempty subset.An easily verifiable necessary and sufficient condition is proposed and the formula is provided to calculate the shortest time.In addition,we extend the obtained results to local synchronization of incomplete-profile switched NEGs.Finally,an illustrative example is given to show the effectiveness of the theoretical results.
switched networked evolutionary gamessynchronizationsemi-tensor product of matricesset stabilityinvariant subsetincomplete-profile
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