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Authors
Ingo Piepers
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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.
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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.
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.
We investigate numerically the clustering behavior of a system of phase oscillators with positive and negative couplings under a periodic external driving field with a bimodal distribution of driving phases. The phase distribution and the mean speed of the traveling state, as well as the order parameter for synchronization, are computed as the driving amplitude is varied. We observe that the periodically-driven system can also host traveling states for parameters in the same range as those for the case of a system without a driving field. The traveling speed is found to depend non-monotonically on the driving amplitude. In particular, oscillators divide into four clusters and move in pairs. Further, depending on the driving amplitude, two kinds of traveling mode arise: pairs of clusters traveling in the same direction (symmetric mode) and in opposite directions (antisymmetric mode). In the latter case (antisymmetric traveling mode), the average phase speed of the whole system apparently vanishes. A phenomenological argument for such behavior is given.
The International System develops according to a clear logic: By means of systemic wars organisational innovations are periodically introduced, contributing to a process of social expansion and integration, and to wealth creation. A finite-time singularity accompanied by four accelerating log-periodic cycles can be identified during the time frame 1495-1945.
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