Numerically evaluated functional equivalence between chaotic dynamics in neural networks and cellular automata under totalistic rules

Abstract

Chaotic dynamics in a recurrent neural network model and in two-dimensional cellular automata, where both have finite but large degrees of freedom, are investigated from the viewpoint of harnessing chaos and are applied to motion control to indicate that both have potential capabilities for complex function control by simple rule(s). An important point is that chaotic dynamics generated in these two systems give us autonomous complex pattern dynamics itinerating through intermediate state points between embedded patterns (attractors) in high-dimensional state space. An application of these chaotic dynamics to complex controlling is proposed based on an idea that with the use of simple adaptive switching between a weakly chaotic regime and a strongly chaotic regime, complex problems can be solved. As an actual example, a two-dimensional maze, where it should be noted that the spatial structure of the maze is one of typical illposed problems, is solved with the use of chaos in both systems. Our computer simulations show that the success rate over 300 trials is much better, at least, than that of a random number generator. Our functional simulations indicate that both systems are almost equivalent from the viewpoint of functional aspects based on our idea, harnessing of chaos.

Chaotic neural network applied to two-dimensional motion control

“…these dynamical features are a necessary (though not sufficient) condition for solving the 2-D mazes. These conclusions are consistent with the conclusions presented in our earlier work (Suemitsu and Nara 2004;Takada et al 2007;. As the functional features do not depend strongly on the detailed structure of models, we can speculate about the usefulness of chaos in general Ethat chaotic dynamics are potentially useful in systems containing large numbers of degrees of freedom to realize robust, adaptive and complex control functions with simple rules.…”

“…Chaotic dynamics in a two-dimensional cellular automata was successfully applied to solving 2-D mazes based on the idea of harnessing of chaos. From the viewpoint of functional aspects, both dynamical models show almost equivalent results (Takada et al 2007). These studies not only indicate that the role of chaos is critically important to realize complex control via simple rules in particular situations, but also enables us to speculate about the usefulness of chaos in general, in the sense that the functional features do not depend strongly on the detailed structure of models.…”