Fuzzy Cognitive Map (FCM) offers many advantages such intuitive knowledge representation and fast numerical reasoning ability, etc. It suits modeling and decision-making of dynamic systems. With the aims to effectively help to analyze and control system sustainable evolution, the paper defines the steady states of fixed point and limited cycle of a FCM modeling system. Accordingly, the rules of steady states of the FCM model and the factors influencing the steady states are presented and proved. The Three-Rivers represents a system including population, ecological environment, social development and their relationships. Based on the relationships, the Three-Rivers ecosystem is modeled by FCM and the Three-Rivers ecosystemsustainable evolutionis analyzed bythe rules of the steady states of FCM.
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