Simulating Complex Systems Complex System Theories, their Behavioural Characteristics and their Simulation Rabia Aziza 1 , Amel Borgi 1 , Hayfa Zgaya 2 and Benjamin Guinhouya 2 1 LIPAH research laboratory, Université de Tunis El Manar, Rommana 1068, Tunis, Tunisia 2 EA 2994, Public Health: Epidemiology and Healthcare Quality, University Lille, 42 rue Ambroise Paré, Loos 59120, Lille, France rabia.aziza@gmail.com, amel.borgi@insat.rnu.tn, {hayfa.zgayabiau, benjamin.guinhouya}@univ-lille2.fr Keywords: Complex Systems, Simulation, Agents, Constructivist Approach. Abstract: Complexity science offers many theories such as chaos theory and coevolutionary theory. These theories illustrate a large set of real life systems and help decipher their nonlinear and unpredictable behaviours. Categorizing an observed Complex System among these theories depends on the aspect that we intend to study, and it can help better understand the phenomena that occur within the system. This article aims to give an overview on Complex Systems and their modelling. Therefore, we compare these theories based on their main behavioural characteristics, e.g. emergence, adaptability, and dynamism. Then we compare the methods used in the literature to model and simulate Complex Systems, and we propose and discuss simple guidelines to help understand one’s Complex System and choose the most adequate model to simulate it. 1 INTRODUCTION Simulation consists of mimicking the operation of a real system in order to understand its behaviour. The more complicated a system, the more difficult it is to simulate. And such is the case of Complex Systems (CSs) that contain a large number of elements with nonlinear behaviours (Obaidat and Papadimitriou, 2003; Lam, 1998). This study presents an overview of the CS theories and compares the methods used to model them. Also, we propose a simple guide that helps in choosing the appropriate model to describe a CS in any domain. The paper is structured as follows. In Section 2, we explain the main behavioural characteristics in a CS and we compare its main theories. In Section 3, we compare the approaches and methods used for modelling CSs. Then, we propose a simple guide for selecting the method that fits the CS to model. Finally, we conclude in Section 4. 2 COMPLEX SYSTEMS The concept of holism considers the system as a whole in order to study its behaviour. The concept “the whole is greater than the sum of its parts”, stated by the Chinese philosopher Confucius, is the heart of the definition of complexity science that refers to the study of CSs. A CS is a set of a large number of interconnected elements that interact with each other and with the environment in a nonlinear way. These elements, called agents, are “active, persistent components that perceive, reason, act, and communicate” (Huhns and Singh, 1998). The behaviour within CSs is nonlinear, non-deterministic and unpredictable. In fact, a CS is guided by a decentralized complex decision-making process, and the complexity is generated by the cooperation of many entities that use their own local rules in order to evolve and interact through a network of feedback loops (Lam, 1998; Nicolet, 2010). 2.1 Behavioural Characteristics A system can be labelled as complex if it expresses a subset of the following behaviours:  Emergence: is the unexpected production of new structures, behaviours or patterns, e.g. the V- shape of a flying flock of birds. Such production was not programmed beforehand. It rather results from the continuous interactions. It can be detected and interpreted by the entities (strong emergence), or by an external observer (weak emergence) (Elsner et al., 2015; Lichtenstein, 2014).