A Study on Emergence of Game and dynamical Complexity by Covpled Dynamical Recog

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The aim of this project was to propose a new model framework to study evolution and cognition dynamics. Some main results are the followings.1. We have studied a model of game players who play a game by generating other player's model by a dynamical recognizer. Based on this model, the prisoner's dilemma game, the Dubey game and artificial discourse dynamics are simulated. We have also discussed an extended version of the Turing test in terms of dynamical systems.2. We have proposed and analyzed a new game system, in which the rule and the strategy are expressed by λ sentences. Since λ calculus doesn't distinguish between rules and startegies, a meta-game system is naturally treated in this system in the sense that rules and strategies can interfer with each other.3. We have studied and analyzed temporal evolution of discourse system based on a coupled dynamical recognizer. This is the first mathematical studies on discourse dynamics and the results will be published within this year.4. A distinction between a rule and a strategy in a game and between syntax and semantics in discourse interaction have been studied by giving the distinction from without. Here we have basically studied the synthetic nature of distinction itself in various systems. Other systems such as membranes and the internal chemical reaction and self/non-self disction of an immune network are studied as well. One of the important aspect both in evolution and cognition is evolvability. I have discussed it intensively.All the work I have done is related to the main theme of complex systems study called Synthetic Complexity. This is the complexity essentially generated from interactions. We should further work on this concept to build a new theoretical framework for evolution and cognition.