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Patterns in the nature often emerge on assembly of many homogeneous subsystems, and are characterized as stationary relationship among subsystem's states. In many cases, subsystem interactions are local, while patterns are de ̄ned throughout the system as a global order. From the engineering point of view, how to achieve a desired global relation with local interactions is a problem to solve for system decentralization. Under this background, Yuasa and Ito (1989) proposed a pattern formation theory in autonomous decentralized system based on the gradient dynamics. In this paper, we extend their method to treat adaptability that autonomous decentralized system is expected to possess. Our concept on adaptation is to decrease subsystem interaction by changing interaction method, which is also based on the gradient dynamics.

An Adaptation Theory in Autonomous Decentralized Systems