Les systèmes socio naturels possèdent la capacité de résister aux aléas. Les catastrophes les perturbent, mais les font rarement disparaître. Le concept de résilience, d’origine physique, qui illustre cette capacité s’est enrichi lors de son transfert dans différentes disciplines scientifiques. Certes, la résilience est difficile à mesurer. Mais sa connaissance permet d’adopter de nouvelles formes de gestion des risques naturels ou sociaux. Ces nouvelles formes de gestion sont très différentes des approches technologiques qui ne sont pas toujours bien adaptées au milieu ou à la société.
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
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