Complexity Theory and Network Centric Warfare (Information by James Moffat

By James Moffat

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Additional resources for Complexity Theory and Network Centric Warfare (Information Age Transformation Series)

Sample text

In a typical natural phenomenon, the number of variables n is expected to be very high. This will considerably complicate the search for all possible solutions. However, suppose that by experiment we know one of the solutions. By a standard method, known as Linear Stability Analysis, we can then determine the parameter values for which this solution regarded as the reference state switches from asymptotic stability to instability. ROBUSTNESS AND LINEAR STABILITY ANALYSIS Stability or “robustness to change” is essentially determined by the response of the system to perturbations.

Different timescales of this type lead to what is termed 1/f noise. 1/f noise is a label used to describe a particular form of time correlation in nature. If a time signal fluctuates in a seemingly erratic way, the question is whether the value of the signal N (τ 0 ) at time τ 0 has any correlation to the signal measured at time τ 0 + τ ( N (τ 0 + τ) ). The amount of causation is characterised by a temporal correlation function: G (τ) = N (τ 0 ) N (τ 0 + τ) Clustering in Space and Time τ0 − N (τ 0 ) 2 τ0 .

Away from the critical temperature, the correlations decay exponentially, G (r ) ~ exp(−r / ξ) , beyond the correlation −ν length ξ . The correlation length diverges, ξ ~ T − Tc , as the critical temperature is approached. e. Clustering in Space and Time Chapter 1 27 G (r ) ~ r − η . The divergence is considered to be the signal of the lack of a characteristic length scale. Self-organising systems may be characterised and examined in this way. CELLULAR AUTOMATA The introduction in 1987 of the Self-Organised Criticality concept employed the language of avalanches (clusters) of sand grains.

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