Investigation of collapse of complex socio-political systems using classical stability theory

Some mighty and prosperous empires of the past collapsed. Explanations why successful civilizations collapsed disagree even about what collapse means. In fields like Physics, Engineering and Biomathematics, collapse is a response of a system in unstable equilibrium to a perturbation. This work applies the mathematical formulation of classical stability theory to study socio-economic collapse. The model illustrates that increasing complexity invariably explains collapse. This finding agrees with other scholars, however the results dispute the need of associated factors like diminishing marginal returns, excessive complexity growth rate or the relationship between frequency of perturbation and their magnitude (references provided). Moreover, in previous works the term complexity envelops a variety of elements. The approach of this work numerically defines complexity. Such a definition allows unambiguously comparing the complexity of various societies. The paper brings an incremental contribution to archaeological and historical debates, by using classical stability theory for modeling complex socio-political systems. Applying classical stability models in society allows a rigorous interpretation of concepts used in archaeology as sustainability (equilibrium) or resiliency (stability). The investigation shows that the transition of a stable equilibrium to an unstable one may take centuries: nevertheless, the failure is abrupt. The article discusses why associating various past societal collapses with a wide range of other causes does not contradict the model. (C) 2019 Elsevier B.V. All rights reserved.