In this talk, our aim is to present the Panic-Control-Reflex system, which is a mathematical model that was built in order to better understand and predict the behavioral reactions of individuals facing a catastrophic event. The geographical background of those specific phenomena naturally brings us to set the problem within the complex systems framework, thus we consider coupled networks of dynamical systems, in both finite and infinite dimensional spaces. Consequently, our work deals with complex networks of ordinary differential equations as well as partial differential equations.
We analyze the effect of behavioral evolution, emotional contagion, linear and quadratic interactions among the population concerned with the catastrophe, and we take additionally into account the effect of the spatial diffusion. We pay a special attention to the panic behavior which is to be avoided and controlled, and analyze in which parameter regimes a persistence of panic can occur.
Furthermore, we explore sufficient conditions on the topology of the graph which determines the structure of the geographical network, in order to reach a synchronization state of every node, in correspondence with the expected return of all individuals to a normal behavior.