Claudio BONANNO, Vincenzo MANCA

Discrete Dynamics in Biological Models

 

Abstract.

A survey of dynamical systems is given that is focused on discrete models and on their biological relevance. After a presentation of general concepts for classical definitions of (deterministic) chaos, symbolic dynamics and cellular automata are analysed with a particular emphasis to Wolfram's and Langton's dynamical classifications. The genetic regulation model of Kauffman's boolean networks is then presented, where the behaviours ``at edge of chaos'' play a crucial role, and some parameters discriminate typical classes of systems. It is argued the importance of discrete models of chaos related to Formal Language Theory, where chaotic unpredictability and ``computational unpredictability'' could be connected.

 

Keywords: Dynamical Systems, Cellular Automata, Symbolic Dynamics, Boolean Networks, Biological Models.