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We are interested in studying the spread of chaos in an interaction network modeled by a Coupled Map Network (CMN). This graph is formed by nodes characterized by a measurable state variable that may exhibit chaotic time series. The interaction between the nodes may propagate their states in the network leading through a coupling process to some synchronization phenomenon which is known as nonlinear oscillator synchronization. The interaction network that we aim to study contains initially only one chaotic node that is responsible of the spread of chaos. Our goal consists then to study how to identify the node which is the source of the spread of chaos in an interaction network and how to detect the set of nodes becoming disturbed by the propagation of the chaotic node state. In this paper, we seek some appropriate measures to quantify the dynamic complexity of the nodes in order to identify the group of chaotic nodes as well as the source of the spread of chaos in the graph. We show by some simulations on random graphs that the Shannon entropy calculated on the close returns plots is an appropriate measure to detect chaotic series from a node. The extension of close returns plots to joint recurrence plots enables to identify the source of the spread of the disturbance in the network.

Most of the work on pedestrian simulations places them in a homogeneous context (emergency evacuation, crossing streets, airport). They do not take into account the many interpedestrian interactions induced by a dynamical environment requiring a contextual adaptation, for instance a situation with a danger perceived. Indeed, to deviate from a dangerous pedestrian, one will accept to get closer to other "normal" pedestrians. Thus, one alters the initial interaction based on his perception of the environment. Based on a moving model, we propose to found an agent pedestrian model that can undertake the contextual and dynamic aspect of interactions between pedestrians.; La plupart des travaux portant sur la simulation de piétons les placent dans un contexte d’interaction inter-piéton quasi homogène (situation d’évacuation, traversée de rue, aéroport). Ils ne prennent pas en compte les multiples interactions inter-piétons induites par un environnement dynamique et nécessitant une adaptation contextuelle, en particulier lors d’une situation de danger perçue. En effet, pour s’écarter d’un piéton dangereux, les piétons vont accepter de se rapprocher les uns des autres. De ce fait, ils modifient l’interaction initiale qu’ils avaient les uns avec les autres en fonction de leur perception de l’environnement. Étant donné un modèle de déplacement, notre proposition vise à poser les bases d’un modèle agent piéton dans le but de pouvoir prendre en compte les aspects contextuels et dynamiques des interactions entre piétons.