Chain Models for Growth Processes/Code Theory

Abstract

Based on the concept of Exponential Towers (1981) dx_i/dt = K_ix_ix_i+1 a Structure Design Principle was introduced which led to the result that a huge class of ordinary differential equations could be represented by the famous Lotka-Volterra Equations,

As suitable models for growth a qualitative analysis of Exponential Towers is given and interpreted in the terms of automata theory and interval mappings. The relation between the so called exponential code and the Exponential Towers is generalised to arbitrary binary codes given by a code generator function z=g(s,K,z’) and leads to a great diversity of dynamic chains with similar properties as we found for Exponential Towers.

Constructing by different approaches vector codes we can imbed the generalised dynamic chains in corresponding networks which are a generalisation of Lotka-Volterra networks offerring new possibilities for time series analysis.