Physica A 350 (2005) 597–610 Analysis and identification of a social interaction model Xi Shen à , Philippe De Wilde Department of Electrical and Electronic Engineering, Imperial College London, South Kensington Campus, Exhibition Road, London SW7 2BT, UK Received 22 September 2004 Available online 7 January 2005 Abstract In this paper, we present a model of social interaction systems. By comparing it with existing analytical models, and using simulations, we focus on dynamical behavior and interaction properties of this nonlinear time-varying system. The system’s behavior can be predicted if we have sufficient knowledge of system parameters such as the connection matrix. Observation of system behavior can be useful to recover the unknown or insufficiently known levels of interaction strength. Furthermore, if proper sampling can be carried out, the system can be identified. This model is suitable for investigating social phenomena such as the fashion phenomenon. r 2005 Elsevier B.V. All rights reserved. PACS: 87.23.Ge; 87.23.Cc; 02.50.Le Keywords: Social interaction; Game theory; Ecosystem; Fashion 1. Introduction Modelling evolutionary complex systems is one of the key approaches in the study of systems such as ecosystems (see e.g. Refs. [1–3]), sociological systems (see e.g. Refs. [4–6]), auction pricing systems (see e.g. Refs. [7,8]), etc. Many models have been developed by defining evolving rules at the level of individuals, and in evolutionary ARTICLE IN PRESS www.elsevier.com/locate/physa 0378-4371/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physa.2004.11.042 à Corresponding author. E-mail address: xi.shen@imperial.ac.uk (X. Shen).