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International audienceThe aim of this paper is to present some mathematical results concerning the PCR system (Panic-Control-Reflex), which is a model for human behaviors during catastrophic events. This model has been proposed to better understand and predict human reactions of individuals facing a brutal catastrophe, in a context of an established increase of natural and industrial disasters. After stating some basic properties, that is positiveness, boundedness, and stability of the solutions, we analyze the transitional dynamic. We then focus on the bifurcation that occurs in the system, when one behavioral evolution parameter passes through a critical value. We exhibit a degeneracy case of a saddle-node bifurcation, in a larger context of classical saddle node bifurcations and saddle-node bifurcations at infinity, and we study the inhibition effect of higher order terms

This chapter proposes to generalize to a geographical context an innovative SIR-based model describing human collective behaviors in situations of disasters. The novelty of this work is to adopt a complex network approach in order to model the influence of the space on the transitions among one behavior and the others. This network model will be applied on the specific case of a tsunami on the French Riviera caused by a seismic event.

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Abstract:The reflections regarding risk and industrial catastrophes question the complexity theories. Besides the new concepts which lead us to question older concepts (risk, hazard and vulnerability), we propose to think about more practical aspects, for example the modelling of human behaviour and the confrontation in crisis situations. The link between concepts as: critical self-organization, emergence, bifurcation, and the methods in the Distributed Artificial Intelligence used to model them is however difficult. In this paper, we present ongoing analysis on the key concepts of risk science, such as the hazards and the catastrophes. We propose to enrich them with complex systems theories. First, we present methodological perspectives of the DAI, for example multi-agent systems, and compare them with other simulation methods used in the context of the risks. Secondly, we present the MOSAIIC model (Modelling and Simulation of Industrial Accidents by Individual-Based methods) which gives possibilities to simulate the behaviour of individuals during an industrial accident. The project and the MOSAIIC model aim to explore the effects of a major industrial accident on public health. For instance, the emission and the spread of a toxic gas in an urban environment may be a serious danger for the human health. Thus we propose to study the consequences of this type of event in order to reduce the vulnerability of the populations. In the model, we emphasize both on spatial and behavioral dimensions (ie. mobility and perception of risk) All these questions lead us to use different methodologies of analysis. For example, concerning mobility, the daily traffic can be simulated at a meso scale: a road axis for example. In that way, we aim to simulate the global dynamics of the network from the modelling of flows on arcs of the network (modulated according to the time of day and the day of week). Yet, we use classical models (for instance equilibrium models) because they give an "average image" of the flows of vehicles on the arcs. Based on this first structural mobility, it is then possible to consider "a change of level" regarding both the representation and the analysis: if a risk occurs or if a specific context disrupts the structure. As a consequence, from a management of flows on the arc, we turn to an analysis of the individual behaviours in a multi-agent system.