Fractional Trajectories: Decorrelation Versus Friction

Abstract

The fundamental connection between fractional calculus and subordination processes is explored and affords a physical interpretation of a fractional trajectory, that being an average over an ensemble of stochastic trajectories. Heretofore what has been interpreted as intrinsic friction, a form of non-Markovian dissipation that automatically arises from adopting the fractional calculus, is shown to be a manifestation of decorrelations between trajectories. We apply the general theory developed herein to the Lotka Volterra ecological model, providing new insight into the final equilibrium state. The relaxation time to achieve this state is also considered.

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Document Details

Document Type
Technical Report
Publication Date
Jul 27, 2013
Accession Number
ADA624914

Entities

People

  • A. Svenkeson
  • B. J. West
  • M. T. Beig
  • Malgorzata Turalska
  • P. Grigolini

Organizations

  • University of North Texas

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Calculus
  • Clocks
  • Complex Systems
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Electronic Mail
  • Equations
  • Friction
  • Internal Friction
  • Nonlinear Systems
  • Observation
  • Probability
  • Probability Distributions
  • Random Variables
  • Statistical Mechanics
  • Time Intervals

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Mathematical Modeling and Probability Theory.
  • Theoretical Analysis.