Dynamical Systems and Interaction Networks

Abstract

This chapter first reviews biological models in the framework of dynamical systems. It then illustrates some basic control-theoretic concepts and definitions used in the study of dynamical systems. The chapter also discusses several dynamical models that are typically used in modeling cellular processes and interactions. It then introduces discrete-time Boolean networks. Artificial neural network (ANN) models were originally used to model the connectivities of neurons in brains. Thus, in contrast to cellular signaling networks, ANN models generally have a less direct one-to-one correspondence to biological data. Piecewise linear (PL) systems are quite powerful in modeling biological systems since they may be used as identification models (by means of piecewise linear approximations), or as controllers for more general systems. An interesting class of biological systems with simpler behaved dynamics are systems with monotone dynamics. The dynamics of a monotone system preserves a specific partial order of its inputs over time.