Can potentially useful dynamics to solve complex problems emerge from constrained chaos and/or chaotic itinerancy?

Abstract

Complex dynamics including chaos in systems with large but finite degrees of freedom are considered from the viewpoint that they would play important roles in complex functioning and controlling of biological systems including the brain, also in complex structure formations in nature. As an example of them, the computer experiments of complex dynamics occurring in a recurrent neural network model are shown. Instabilities, itinerancies, or localization in state space are investigated by means of numerical analysis, for instance by calculating correlation functions between neurons, basin visiting measures of chaotic dynamics, etc. As an example of functional experiments with use of such complex dynamics, we show the results of executing a memory search task which is set in a typical ill-posed context. We call such useful dynamics "constrained chaos," which might be called "chaotic itinerancy" as well. These results indicate that constrained chaos could be potentially useful in complex functioning and controlling for systems with large but finite degrees of freedom typically observed in biological systems and may be such that working in a delicate balance between converging dynamics and diverging dynamics in high dimensional state space depending on given situation, environment and context to be controlled or to be processed.

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

“…We confirmed that chaotic dynamics introduced in the network does not so sensitively depend on the size of the neuron number (Nara 2003). However, if N is too small, chaotic dynamics can not occur; whereas if N is oversized, it results in excessive computing time.…”

“…This method was confirmed to be effective to avoid spurious attractors that affect L attractors with K-step maps embedded in the network when connectivity r = N (Nara andDavis 1992, 1997;Nara et al 1993Nara et al , 1995Nara 2003;Suemitsu and Nara 2003).…”

“…In order to investigate the dynamical structure, we calculated basin visiting measures and it suggests that the trajectory can pass the whole N-dimensional state space, that is, cyclic memory attractors ruin due to a quite small connectivity (Nara andDavis 1992, 1997;Nara et al 1993Nara et al , 1995Nara 2003;Suemitsu and Nara 2003).…”

“…Artificial neural networks for chaotic itinerancy were studied with great interests (Aihara et al 1990;Tsuda 1991Tsuda , 2001Kaneko and Tsuda 2003;Fuji et al 1996). As one of those works, by Nara and Davis, chaotic dynamics was introduced in a recurrent neural network model (RNNM) consisting of binary neurons, and for investigating the functional aspects of chaos, they have applied chaotic dynamics by means of numerical methods to solving, for instance, a memory search task which is set in an ill-posed context (Nara andDavis 1992, 1997;Nara et al 1993Nara et al , 1995Kuroiwa et al 1999;Suemitsu and Nara 2003). In their papers, they proposed that chaotic itinerancy could be potentially useful dynamics to solve complex problem, such as ill-posed problems.…”

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

“…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.…”