Chaotic dynamics introduced into a neural network model is applied to solving two-dimensional mazes, which are ill-posed problems. A moving object moves from the position at t to t + 1 by simply defined motion function calculated from firing patterns of the neural network model at each time step t. We have embedded several prototype attractors that correspond to the simple motion of the object orienting toward several directions in two-dimensional space in our neural network model. Introducing chaotic dynamics into the network gives outputs sampled from intermediate state points between embedded attractors in a state space, and these dynamics enable the object to move in various directions. System parameter switching between a chaotic and an attractor regime in the state space of the neural network enables the object to move to a set target in a two-dimensional maze. Results of computer simulations show that the success rate for this method over 300 trials is higher than that of random walk. To investigate why the proposed method gives better performance, we calculate and discuss statistical data with respect to dynamical structure.
A time delayed effect in a recurrent neural network model was investigated, where the model is constructed on the binary states of each neuron and on the discrete time development. The time delay is assumed to be of integer multiple numbers in the unit of updating the time step. The model not only has a function of conventional associative memory, but also enables us to embed a new kind of multiple attractor which cannot be realised in the model without a time delayed effect. Furthermore, by means of numerical simulation, we have found that chaotic dynamics can occur in our model, and that there are a few functioning examples which are superior to the case without a time delayed effect.
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 dynamics in systems having many degrees of freedom are investigated from the viewpoint of harnessing chaos and is applied to complex control problems to indicate that chaotic dynamics has potential capabilities for complex control functions by simple rule(s). An important idea is that chaotic dynamics generated in these systems give us autonomous complex pattern dynamics itinerating through intermediate state points between embedded designed attractors in high-dimensional state space.A key point is 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 set context is one of typical ill-posed problems, is solved with the use of chaos in a recurrent neural network model. Our computer experiments show that the success rate over several hundreds trials is much better, at least, than that of a random number generator. Our functional simulations indicate that harnessing of chaos is one of essential ideas to approach mechanisms of brain functions.
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