Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
1999-07-20
Nonlinear Sciences
Adaptation and Self-Organizing Systems
41 pages, 14 figeres
Scientific paper
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.
Kaneko Kazuhisa
Kataoka Naoto
No associations
LandOfFree
Functional Dynamics II : Syntactic Structure does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Functional Dynamics II : Syntactic Structure, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Functional Dynamics II : Syntactic Structure will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-438675