Asynchrony induces stability in cellular automata based models

Two cellular automata based computer simulations: an immune network model on one hand and the classical game of life on the other hand, despite similar algorithmic presentations, exhibit surprisingly distinct time evolution: respectively a fixed point and the complex dynamics characteristic of class IV cellular automata. At the conclusion of a complete investigation to understand better which of the algorithmic dif ferences is responsible for this behavioural dif ference, we provide evidence that asynchronous rather than synchronous updating turns out to be the key factor . Experimenting and discussing in more detail this stability induction, we show that the responsibility of asynchrony for freezing game of life type of simulation can be theoretically justified in some particular cases by finding an associate L yapunov function whose monotonous tendency proves the stability . The implications of such sensitivity to the updating mechanism for the future of cellular automata based models are reviewed.

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