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Ingo Piepers
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Various self-organized characteristics of the international system can be identified with the help of a complexity science perspective. The perspective discussed in this article is based on various complexity science concepts and theories, and concepts related to ecology and ecosystems. It can be argued that the Great Power war dynamics of the international system in Europe during the period 1480-1945, showed self-organized critical (SOC) characteristics, resulting in a punctuated equilibrium dynamic. It seems that the SOC-characteristics of the international system and the punctuated equilibrium dynamic were - in combination with chaotic war dynamics - functional in a process of social expansion in Europe. According to a model presented in this article, population growth was a component of the driving force of the international system during this time frame. The findings of this exploratory research project contradict with generally held opinions in International Relations theory.
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Motivated by recent experimental and computational results that show a motility-induced clustering transition in self-propelled particle systems, we study an individual model and its corresponding Self-Organized Hydrodynamic model for collective behaviour that incorporates a density-dependent velocity, as well as inter-particle alignment. The modal analysis of the hydrodynamic model elucidates the relationship between the stability of the equilibria and the changing velocity, and the formation of clusters. We find, in agreement with earlier results for non-aligning particles, that the key criterion for stability is $(rho v(rho))> 0$, i.e. a non-rapid decrease of velocity with density. Numerical simulation for both the individual and hydrodynamic models with a velocity function inspired by experiment demonstrates the validity of the theoretical results.
The assumption that complex systems function optimally at the edge of chaos seems applicable to the international system as well. In this paper I argue that the normal chaotic war dynamic of the European international system (1495-1945) was temporarily (1657-1763) interrupted by a more simplified dynamic, resulting in more intense Great Power wars and in a delay of the reorganization of the international system in the 18th century.
The risk of systemic war seems dependant on the level of criticality and sensitivity of the International System, and the systems conditions. The level of criticality and sensitivity is dependant on the developmental stage of the International System. Initially, following a systemic war, the increase of the level of criticality and sensitivity go hand in hand. However, at a certain stage the sensitivity of the International System for larger sized wars decreases; as a consequence of a network effect, we argue. This network effect results in increased local stability of the System. During this phase the criticality of the International System steadily increases, resulting in a release deficit. This release deficit facilitates a necessary build up of energy to push the International System, by means of systemic war, into a new stability domain. Systemic war is functional in the periodic rebalancing of an anarchistic international system.
From the perspective developed in this paper, it can be argued that exponential population growth resulted in the exponential decrease of the life-span of consecutive stable periods during the life-span of the European international system (1480-1945). However, it becomes evident as well that population growth as such is not a sufficient condition to generate a punctuated equilibrium dynamic in the war dynamics of the international system: other conditions and factors - and their interplay - contribute to this typical dynamic as well. From 1945 until the collapse of the Soviet Union (1991), the conditions of international system differed fundamentally from the conditions of the European international system during the period 1480-1945. It can be argued, that sooner or later a punctuated equilibrium war dynamic will resume.
It has been proposed that adaptation in complex systems is optimized at the critical boundary between ordered and disordered dynamical regimes. Here, we review models of evolving dynamical networks that lead to self-organization of network topology based on a local coupling between a dynamical order parameter and rewiring of network connectivity, with convergence towards criticality in the limit of large network size $N$. In particular, two adaptive schemes are discussed and compared in the context of Boolean Networks and Threshold Networks: 1) Active nodes loose links, frozen nodes aquire new links, 2) Nodes with correlated activity connect, de-correlated nodes disconnect. These simple local adaptive rules lead to co-evolution of network topology and -dynamics. Adaptive networks are strikingly different from random networks: They evolve inhomogeneous topologies and broad plateaus of homeostatic regulation, dynamical activity exhibits $1/f$ noise and attractor periods obey a scale-free distribution. The proposed co-evolutionary mechanism of topological self-organization is robust against noise and does not depend on the details of dynamical transition rules. Using finite-size scaling, it is shown that networks converge to a self-organized critical state in the thermodynamic limit. Finally, we discuss open questions and directions for future research, and outline possible applications of these models to adaptive systems in diverse areas.
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