On the network analysis of the state space of discrete dynamical systems

TL;DR

This paper critiques a previous network analysis approach to discrete dynamical systems, highlighting errors in theoretical analysis and limitations of proposed indicators in distinguishing system complexity.

Contribution

It identifies flaws in earlier theoretical analyses and demonstrates that certain network indicators are ineffective for assessing complexity in 1-D Cellular Automata.

Findings

Some theoretical analyses are incorrect.

Proposed network indicators cannot differentiate complexity in 1-D Cellular Automata.

Highlights the need for more accurate measures of dynamical complexity.

Abstract

This paper discusses the letter entitled "Network analysis of the state space of discrete dynamical systems" by A. Shreim et al. [Physical Review Letters, 98, 198701 (2007)]. We found that some theoretical analyses are wrong and the proposed indicators based on two parameters of the state-mapping network cannot discriminate the dynamical complexity of the discrete dynamical systems composed of a 1-D Cellular Automata.