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We consider the general properties of the replicator dynamical system from the stand- point of its evolution and stability. Vector field analysis as well as spectral properties of such system has been studied. A Lyaponuv function for the investigation of the evolution of the system has been proposed. The generalization of replicator dynamics to the case of multi-agent systems is introduced. We propose a new mathematical model to describe the multi-agent interaction in complex system.

Replicator Dynamics and Mathematical Description of Multi-Agent Interaction in Complex Systems