Influencing emotional behavior in a social network

Mankind has always sought out social interaction, and our social interactions influence our thoughts and actions. As technological advances in social media provide a means for more rapid, convenient, and widespread communication, our resulting social interactions can lead to a more dynamic influence. Underlying these interactions are emotional responses to different stimuli and a desire not to become isolated from peers. In this paper, such social interactions are modeled as an undirected graph where each vertex represents an individual and each edge represents a social bond between individuals. Motivated by the non-local property of fractional-order systems, the emotional response of individuals in the network is modeled by fractional-order dynamics whose states depend on influences from social bonds. A decentralized control method is then developed to manipulate the social group to a common emotional state while maintaining existing social bonds (i.e., without isolating peers in the group). Mittag-Leffler stability methods are used to prove asymptotic convergence to a common equilibrium point (i.e., emotional state) of the networked fractional-order system.