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Register a new userThe International System: At the Edge of Chaos
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Authors
Ingo Piepers
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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.
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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.
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.
We focus on a linear chain of $N$ first-neighbor-coupled logistic maps at their edge of chaos in the presence of a common noise. This model, characterised by the coupling strength $epsilon$ and the noise width $sigma_{max}$, was recently introduced by Pluchino et al [Phys. Rev. E {bf 87}, 022910 (2013)]. They detected, for the time averaged returns with characteristic return time $tau$, possible connections with $q$-Gaussians, the distributions which optimise, under appropriate constraints, the nonadditive entropy $S_q$, basis of nonextensive statistics mechanics. We have here a closer look on this model, and numerically obtain probability distributions which exhibit a slight asymmetry for some parameter values, in variance with simple $q$-Gaussians. Nevertheless, along many decades, the fitting with $q$-Gaussians turns out to be numerically very satisfactory for wide regions of the parameter values, and we illustrate how the index $q$ evolves with $(N, tau, epsilon, sigma_{max})$. It is nevertheless instructive on how careful one must be in such numerical analysis. The overall work shows that physical and/or biological systems that are correctly mimicked by the Pluchino et al model are thermostatistically related to nonextensive statistical mechanics when time-averaged relevant quantities are studied.
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.
Self-adjusting, or adaptive systems have gathered much recent interest. We present a model for self-adjusting systems which treats the control parameters of the system as slowly varying, rather than constant. The dynamics of these parameters is governed by a low-pass filtered feedback from the dynamical variables of the system. We apply this model to the logistic map and examine the behavior of the control parameter. We find that the parameter leaves the chaotic regime. We observe a high probability of finding the parameter at the boundary between periodicity and chaos. We therefore find that this system exhibits adaptation to the edge of chaos.
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