Non identical coupled networks with a geographical model for human behaviors during catastrophic events

Guillaume Cantin (1)

1 LMAH - Laboratoire de Mathématiques Appliquées du Havre

The purpose of this work is to study coupled networks of non identical instances of the PCR system (Panic-Control-Reflex), which is a geographical model for human behaviors during catastrophic events. We endow the subsequent graph with superposed linear and quadratic couplings, and explore the effect of the topology of the network on the dynamics of each node. Especially, we investigate the possibility of controlling the panic level in the network by a clever disposal of the connections. We establish a necessary and sufficient condition for synchronization, without any reductive assumption on the nature of the network, and study the global stability of the trivial equilibrium. We illustrate our theoretical results by numerical simulations of randomly generated networks.

Mots clés: PCR system; coupled network; global stability; synchronization

Domaines: Mathématiques [math]

Guillaume Cantin. Non identical coupled networks with a geographical model for human behaviors during catastrophic events. 2017. ⟨hal-01673706⟩