Animal Spirits in Population Spatial Dynamics

Abstract

Collective behavior of herding animals displays a balance between conservative cohesive forces and ”‘innovation’”, or moving towards a goal, as described by Couzin in 2005 (2005). We have given these forces a quantitative mathematical form that is amenable to numerical simulation. The simulations described herein reproduce the phenomena that Couzin observed and indicate that a nearly 5 per cent critical mass is sufficient to pull the whole population along, but smaller innovative teams fail to attract a substantial following. The resulting non-linear dynamic equations have been applied also to modeling of financial market dynamics, where they are seen to produce financial catastrophes by internal population dynamics alone, without any need for external forcing. The equations can thereby also be interpreted as a model of John Maynard Keynes’ Animal Spirits (1936) that are often evoked to describe market psychology.