Historical dynamics of the Chinese dynasties

Sabin Roman

doi:10.1016/j.heliyon.2021.e07293

Abstract

We develop a framework for studying state division and unification, and as a case study we focus on modelling the territorial patterns in imperial China during periods of unity and upheaval. As a modelling tool we employ discrete dynamical systems and analyse two models: the logistic map and a new class of maps, which we name ren maps. The critical transitions exhibited by the models can be used to capture the process of territorial division but also unification. We outline certain limitations of uni-modal, smooth maps for our modelling purposes and propose ren maps as an alternative, which we use to reproduce the territorial dynamics over time. As a result of the modelling we arrive at a quantitative measure for asabiyyah, a notion of group solidarity, whose secular cycles match the historical record over 1800 years, from the time of the Warring States to the beginning of the Ming dynasty. Furthermore, we also derive an equation for aggregate asabiyyah which can be employed in other cases of interest.

Highlights

Lorenz discovered chaos in its modern mathematical sense when he analyzed a set of ordinary differential equations derived from a model of thermal convection (Lorenz, 1963)
Significant progress has been made in modelling social dynamics using ordinary differential equations, in particular for ancient societies (Brander and Taylor, 1998; Roman et al, 2017; Kuil et al, 2016; Roman et al, 2018; Anderies, 1998; Roman and Palmer, 2019), but discrete systems or maps have rarely been employed despite showing rich dynamical behaviour, including chaotic behaviour in one dimension (May, 1976; Feigenbaum, 1978)
We present a mathematical framework for modelling alternating periods of stability and disorder using discrete dynamical systems

Summary

Introduction

Lorenz discovered chaos in its modern mathematical sense when he analyzed a set of ordinary differential equations derived from a model of thermal convection (Lorenz, 1963). Chaos theory has been a focal point of research in dynamical systems, with sustained efforts to apply its insights in the case of social phenomena (Kiel and Elliott, 1996; Robertson and Combs, 2014), but finding robust patterns has proven challenging. We present a mathematical framework for modelling alternating periods of stability and disorder using discrete dynamical systems. The change of dynasties and the alternating cycle between periods of stability and upheaval has led to several theories attempting to explain these historical patterns, a wellknown example being the dynastic cycle (Meskill, 1965; Elvin, 1973)

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