摘要： Complex adaptive system with Agent’s behavior and Agent’s local topological configuration co-evolved has several dynamical Local-Worlds changing due to Agents’ behavior, the optimal strategy in a stable system structure and the invariable distribution of the optimal strategies in a dynamical system structure are the most important to master the property of the system. To draw a conclusion about this, a stochastic differential game, the cooperative stochastic differential game between agents in a same Local-World and non-cooperative stochastic differential game between agents in different Local-Worlds be included, is constructed to describe Agents’ behavior in short time-scale, then a Markov process, whose state consists Agent’s behavior and Agent’s local graphic topology configuration, 6 sub-processes coupled with 6 different behaviors included, is constructed to describe the interaction property in dynamical case. After resolve the optimal strategy in the short time-scale, for arbitrary configuration, by coupling the Nash equilibrium solution of non-cooperative game and Pareto optimal strategy of cooperative game by a non-linear operator, the maximum payoff coupled with the optimal strategy in short time-scale should be introduced to design the preferential attachment mechanism and growth mechanism. Then, the invariable distribution of the system can be obtained by invoking the method of stochastic process. It is conclude that: (1) in the short time-scale, the optimal strategy of arbitrary agents can be determined by considering the character of the cooperative/non-cooperative stochastic differential game, furthermore, the optimal strategy of coupled game can converge into a certain attractor that decide the optimal property in this time-scale. (2) in the long time-scale, agent decides its owner behavior according to the evolution way of random complex networks that driven by preferential attachment and volatility mechanism with its payment, which makes this complex adaptive system evolve, the corresponding invariant distribution can be determined by agents’ behaviors, system’s topology configuration, the noise of agent’s behavior and the system population; when the behavior noise tend to 0 the invariant distribution can converge into a certain rate function, however, when the population ten to infinity, the invariant distribution can converge into another ratio function, so, small noise of behavior is not identical to large population as far as this system is considered.