Physica D 204 (2005) 70–82 Ordered asynchronous processes in multi-agent systems David Cornforth a,∗ , David G. Green b , David Newth a,c a School of Environmental and Information Sciences, Charles Sturt University, P.O. Box 789, Albury, NSW 2640, Australia b School of Computer Science and Software Engineering, Monash University, Clayton, Vic. 3800, Australia c CSIRO Centre for Complex Systems Science, GPO Box 284, Canberra, ACT, Australia Received 7 April 2004; received in revised form 1 February 2005; accepted 6 April 2005 Communication by S. Kai Abstract Models of multi-agent systems usually update the states of all agents synchronously, but in many real life systems, agents behave asynchronously. Relatively little is yet known about the dynamic characteristics of asynchronous systems. Here we compare synchronous, random asynchronous, and ordered asynchronous updating schemes. Using one-dimensional (1D) cellular automata as a case study, we show that the type of update scheme strongly affects the dynamic characteristics of the system. We also show that global synchronisation can arise from local temporal coupling. Furthermore, it is possible to switch between chaotic, cyclic and modular behaviour by varying a single parameter, which suggests a possible mechanism by which environmental parameters influence emergent structure. We conclude that ordered asynchronous processes with local temporal coupling play a role in self-organisation within many multi-agent systems. © 2005 Elsevier B.V. All rights reserved. PACS: 05.45.Xt; 05.65.+b; 07.05.Tp; 89.75.Fb Keywords: Asynchronous; Multi-agent; Cellular automata; Models 1. Introduction From crystal lattices to human societies, many nat- ural and artificial phenomena can be represented as multi-agent systems. In general, multi-agent systems ∗ Corresponding author. Tel.: +61 2 6051 9652; fax: +61 2 6051 9897. E-mail addresses: dcornforth@csu.edu.au (D. Cornforth), david.green@csse.monash.edu.au (D.G. Green), david.newth@csiro.au (D. Newth). consist of simple processing elements, or agents (such as atoms, cells or people), and the links between the agents that form a network [1]. Common rep- resentations include cellular automata (CA), random Boolean networks (RBNs) and artificial neural net- works (ANNs). Studies have shown that these systems display a rich variety of behaviour, including stable points, cycles, complexity and chaos. Models of multi-agent systems have traditionally treated time as discrete and state updates as occurring synchronously and in parallel. Implicitly, they assume 0167-2789/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physd.2005.04.005