Scaling of fluctuations in complex dynamics

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Scaling of fluctuations in complex dynamics

• Zoltán Eisler
• János Kertész
• Budapest University of Technology and Economics,
• Dept. of Theoretical Physics

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What makes a system complex?

• Many, interacting elements
• Internet
• society
• economy

? not all have good models Time series
analysis! How?
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A practical method

• Elements of a complex system i1N
• Measured activity (positive, additive quantity)
  fi(t)
• servers ? data traffic (bytes/min)
• companies ? trading activity (USD/min)
• mean activity
• std. dev. (fluctuations)

?
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• If the dynamics is a sum of many, equivalent,
  independent events (data packets)
• Central limit theorem
• i different servers!

a1/2
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• fluctuations not dominated by internal, diffusive
  processes
• external factor the total number of total
  vehicles varies from day to day

a1
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1/2ltalt1
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The point is

• Empirical method based on a simple scaling law
• a can be measured, even for exotic systems,
  without the assumption of any model
• The value of a gives you hints on the systems
  dynamics

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Thanks!

• 1 M.A. Menezes and A.-L. Barabási, PRL 92,
  28701 (2004)
• 2 Z.E. et al, EPL 69, 664-670 (2005)
• 3 Z.E., J. Kertész, PRE 71, 057104 (2005)
• 4 Z.E., J. Kertész, PRE 73, 046109 (2006)
• 5 Z.E., J. Kertész, EPJB 51, 145-154 (2006)