Functional Dynamics II : Syntactic Structure
| dc.creator | Kataoka, N. | |
| dc.creator | Kaneko, K. | |
| dc.date | 1999-07-20 | |
| dc.date.accessioned | 2026-07-07T01:51:05Z | |
| dc.date.available | 2026-07-07T01:51:05Z | |
| dc.description | Functional dynamics, introduced in a previous paper, is analyzed, focusing on the formation of a hierarchical rule to determine the dynamics of the functional value. To study the periodic (or non-fixed) solution, the functional dynamics is separated into fixed and non-fixed parts. It is shown that the fixed parts generate a 1-dimensional map by which the dynamics of the functional values of some other parts are determined. Piecewise-linear maps with multiple branches are generally created, while an arbitrary one-dimensional map can be embedded into this functional dynamics if the initial function coincides with the identity function over a finite interval. Next, the dynamics determined by the one-dimensional map can again generate a `meta-map', which determines the dynamics of the generated map. This hierarchy of meta-rules can continue recursively. It is also shown that the dynamics can produce `meta-chaos' with an orbital instability that is stronger than exponential. The relevance of the generated hierarchy to biological and language systems is discussed, in relation with the formation of syntax of a network. | |
| dc.description | 41 pages, 14 figeres | |
| dc.identifier | https://arxiv.org/abs/adap-org/9907005 | |
| dc.identifier | http://arxiv.org/abs/adap-org/9907005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/204 | |
| dc.subject | Adaptation and Self-Organizing Systems | |
| dc.title | Functional Dynamics II : Syntactic Structure | |
| dc.type | text |