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• W89151117 abstract "This article presents some prototypes of conflict situations that follow from different pathways to chaos. The substance of the conflicts can be extracted from empirical analysis using orbital decomposition (symbolic dynamics), nonlinear regression, or simulations, depending on the nature of the problem. Examples from the political science literature are presented. A distinction is also made between conflicts that are centered in chaos and those that are more similar to the hysteresis feature of catastrophe models. Introduction Nonlinear dynamical systems theory (NDS) consists of a group of mathematical concepts for explaining and predicting how events change over time and the interrelationships among those concepts. The primary NDS phenomena are attractors, bifurcations, chaos, fractals, self-organization, catastrophes, and agent-based models. shows up in numerous political writings, denoting a state of disorganization, which is often in contrast to an old order of things that no longer exists. The objective of this article is to explain some of the formalities of mathematical chaos and some applications where relationship of chaos to conflict situations have been studied, and to isolate prototypic patterns of chaotic events that are inherent in some conflict situations. Before continuing it is fair to point out that there are other NDS constructs that are useful in explaining some types of conflict situations. For instance agent-based models illustrate how individuals working in their own self-interest produce self-organized systems as they interact with other individuals. Selforganized systems often manifest sudden and discontinuous changes that are recognized as catastrophes or phase shifts (Guastello, 2002). Competition-cooperation dynamics are often inherent in those dynamics (Axelrod, 1984; Maynard-Smith, 1982). Chaos Chaos is a phenomenon that we can observe in a time series of events where seemingly random events are predictable with simple but special equations. The phenomenon was first discovered by Henri Poincare, a physicist, who was trying to solve the three-body problem in the 1890s: If we have a speck of dust moving between two gravitational forces, what is the particle's path of movement? He concluded that the path would be very complex, such that the mathematics needed to describe it did not exist at the time. Chaos regained notoriety in the early 1960s, when Edward Lorenz (1963), a meteorologist was studying weather patterns using variations of equations for turbulent flows of air or water. He discovered that very small differences in initial states ofthe weather system could produce some very different results and patterns. This is the principle oi sensitivity to initial conditions, which became known soon afterwards as the butterfly effect (Smith, 2007; Sprott, 2003). A substantial amount of mathematical research on chaos was performed soon afterwards, and seemed to reach its peak in the 1980s. Most ofthe fundamental applications of chaos for explaining events in the social sciences started in the early 1990s. Chaos has three distinctive features. The first is non-repeating sequences; an exam- ple appears in Figure 1 . The second is bounded- ness; the values ofthe variable being observed stays within a fixed range, even though the movement within the range is unpredictable. The first two properties are really matters of degree. The third feature is sensitivity to initial conditions: Two points start arbitrarily close together, but become far apart as iteration progresses. Iteration is a computational technique of starting with a number, running it through an equation, taking the result and running it through the same equation again, running the next result through the equation, and so on. It is convenient to regard the behavior of living systems over time as computations, even if the organism is not consciously doing any math. Pathways to Chaos and Conflict There are three basic pathways by which a system can become chaotic. …" @default.
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• W89151117 date "2008-10-01" @default.
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• W89151117 title "Chaos and Conflict: Recognizing Patterns" @default.
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