Free Access
Math. Model. Nat. Phenom.
Volume 10, Number 3, 2015
Model Reduction
Page(s) 48 - 60
Published online 22 June 2015
  1. E. Barkai, R. Metzler, J. Klafter. From continuous time random walks to the fractional Fokker-Planck equation. Physical Review E, 61 (1) (2000), 132–138. [Google Scholar]
  2. S. Fedotov. Subdiffusion, chemotaxis, and anomalous aggregation. Physical Review E, 83 (2) (2011), 1–5. [CrossRef] [Google Scholar]
  3. S. Fedotov. Nonlinear subdiffusive fractional equations and the aggregation phenomenon. Physical Review E, 88 (3) (2013), 032104. [CrossRef] [Google Scholar]
  4. S. Fedotov, S. Falconer. Subdiffusive master equation with space-dependent anomalous exponent and structural instability. Physical Review E, 85 (3) (2012), 1–6. [CrossRef] [Google Scholar]
  5. S. Fedotov, S. Falconer. Random death process for the regularization of subdiffusive fractional equations. Physical Review E, 87 (5) (2013), 052139. [CrossRef] [Google Scholar]
  6. S. Fedotov, S. Falconer. Nonlinear degradation-enhanced transport of morphogens performing subdiffusion. Physical Review E, 89 (1) (2014), 012107. [CrossRef] [Google Scholar]
  7. S. Fedotov, A. Ivanov, A.Y. Zubarev. Non-homogeneous random walks, subdiffusive migration of cells and anomalous chemotaxis. Mathematical Modelling of Natural Phenomena, 8 (2) (2013), 28–43. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  8. S. Fedotov, N. Korabel. Subdiffusion in an external potential: Anomalous effects hiding behind normal behavior. Physical Review E, 91 (2015), 042112. [CrossRef] [MathSciNet] [Google Scholar]
  9. S. Fedotov, V. Méndez. Non-Markovian model for transport and reactions of particles in spiny dendrites. Physical Review Letters, 101 (2008), 218102. [CrossRef] [PubMed] [Google Scholar]
  10. S. Havlin, D. Movshovitz, B. Trus, G.H. Weiss. Probability densities for the displacement of random walks on percolation clusters. Journal of Physics A, 18 (12) (1985), L719. [CrossRef] [Google Scholar]
  11. T. Hillen, K. Painter. Global existence for a parabolic chemotaxis model with prevention of overcrowding. Advances in Applied Mathematics, 26 (4) (2001), 280–301. [CrossRef] [MathSciNet] [Google Scholar]
  12. T. Hillen, K.J. Painter. A user’s guide to pde models for chemotaxis. Journal of Mathematical Biology, 58 (1-2) (2009), 183–217. [Google Scholar]
  13. S.T. Johnston, M.J. Simpson, R.E. Baker. Mean-field descriptions of collective migration with strong adhesion. Physical Review E, 85 (5) (2012), 051922. [CrossRef] [Google Scholar]
  14. M.M. Meerschaert, P. Straka. Semi-Markov approach to continuous time random walk limit processes. The Annals of Probability, 42 (4) (2014), 1699–1723. [CrossRef] [MathSciNet] [Google Scholar]
  15. V. Mendéz, S. Fedotov, W. Horsthemke. Reaction-transport systems: Mesoscopic foundations, fronts, and spatial instabilities. Springer, 2010. [Google Scholar]
  16. R. Metzler, J. Klafter. The random walk’s guide to anomalous diffusion: A fractional dynamics approach. Physics Reports, 339 (1) (2000), 1–77. [Google Scholar]
  17. R. Metzler, J. Klafter, I.M. Sokolov. Anomalous transport in external fields: Continuous time random walks and fractional diffusion equations extended. Physical Review E, 58 (2) (1998), 1621–1633. [NASA ADS] [CrossRef] [Google Scholar]
  18. M. Raberto, E. Scalas, F. Mainardi. Waiting-times and returns in high-frequency financial data: an empirical study. Physica A: Statistical Mechanics and its Applications, 314 (2002), 749–755. [Google Scholar]
  19. M. Rausand, A. Høyland. System reliability theory: Models, statistical methods, and applications. Wiley Series in Probability and Statistics - Applied Probability and Statistics Section. Wiley, 2004. [Google Scholar]
  20. F. Santamaria, S. Wils, E. De Schutter, G.J. Augustine. The diffusional properties of dendrites depend on the density of dendritic spines. European Journal of Neuroscience, 34 (4) (2011), 561–568. [CrossRef] [Google Scholar]
  21. M.J. Saxton. Anomalous subdiffusion in fluorescence photobleaching recovery: A Monte Carlo study. Biophysical Journal, 81 (4) (2001), 2226–40. [CrossRef] [PubMed] [Google Scholar]
  22. H. Scher, E.N. Montroll. Anomalous transit-time dispersion in amorphous solids. Physical Review B, 12 (6) (1975), 2455–2477. [Google Scholar]
  23. P. Straka, S. Fedotov. Transport equations for subdiffusion with nonlinear particle interaction. Journal of Theoretical Biology, 366 (2015), 71–83. [Google Scholar]
  24. M. Vlad, J. Ross. Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: Application to the theory of Neolithic transition. Physical Review E, 66 (6) (2002), 1–11. [Google Scholar]
  25. A. Yadav, W. Horsthemke. Kinetic equations for reaction-subdiffusion systems: Derivation and stability analysis. Physical Review E, 74 (6), 2006. [Google Scholar]

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