A Solution for Two-Dimensional Mazes with Use of Chaotic Dynamics in a Recurrent Neural Network Model

Abstract

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.

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

“…The first is the converged case into the originally given pattern dynamics (attractor regime) (Kuroiwa et al 2005), the second is the itinerant chaotic dynamics that are not so far from the original pattern dynamics (weakly chaotic regime), and the third is highly developed chaotic dynamics (strongly chaotic regime) (Tamura et al 2003). These would surely be related to complex dynamics occurring in a recurrent neural network model extensively investigated by one of the authors in Mikami and Nara (2003), Nara (2003), and Suemitsu and Nara (2004). Such attractor and/or chaotic dynamics in NN and CA give us the complex pattern dynamics sampled from intermediate state points between embedded patterns in the high-dimensional state space.…”

“…For instance, Nara and Davis have been studying the functional role of chaotic dynamics in a recurrent neural network of binary neurons (abbreviated as NN hereafter) (Davis and Nara 1990;Nara and Davis 1992;Nara et al 1995;Mikami and Nara 2003;Nara 2003;Suemitsu and Nara 2004). They have also shown, in their series of papers, that complex dynamics generated by Cellular Automata (abbreviated as CA hereafter) could be useful in the sense that CA can describe or reproduce arbitrarily given or observed complex dynamics with use of the rule dynamics of CA.…”

Novel tracking function of moving target using chaotic dynamics in a recurrent neural network model

“…Although chaotic dynamics could not always solve all complex problems with better performance, better results often were often observed on using chaotic dynamics to solve certain ill-posed problems, such as tracking a moving target and solving mazes (Suemitsu and Nara 2004). From results of the computer simulation, we can state the following several points.…”

“…For small connectivities from 1 to 60, the network takes chaotic wandering. During this wandering, we have taken a statistics of continuously staying time in a certain basin (Suemitsu and Nara 2004) and evaluated the distribution p(l,l) which is defined by pðl; lÞ ¼fthe number of l jSðtÞ 2 b l in s t s þ l and Sðs À 1Þ 6 2 b l and Sðs þ l þ 1Þ 6 2 b l ; ljl 2 ½1; L g…”

“…Therefore, in order to investigate the brain from functional aspects, we try to construct a model to approach insect behaviours to solve ill-posed problems. As one of functional examples, chaotic dynamics introduced in a recurrent network model was applied to solving a two-dimensional maze, which is set as an ill-posed problem (Suemitsu and Nara 2004). A simple coding method translating the neural states into motion increments and a simple control algorithm adaptively switching a system parameter to produce chaotic itinerant behaviours are proposed.…”