Diese Präsentation wurde erfolgreich gemeldet.
Die SlideShare-Präsentation wird heruntergeladen. ×

# fractional dynamics on networks

Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Nächste SlideShare
Complexity and Freedom
Wird geladen in …3
×

1 von 9 Anzeige

# fractional dynamics on networks

for fractional club meeting at brown on 10/28/2014

for fractional club meeting at brown on 10/28/2014

Anzeige
Anzeige

## Weitere Verwandte Inhalte

Anzeige

### fractional dynamics on networks

1. 1. Fractional dynamics on networks:! anomalous diffusion! and! Levy flights To present at the fractional club meeting! on 10/27/2014 by Summer Zheng Presenting the paper 'Fractional dynamics on networks: Emergence of anomalous diffusion and Levy flights' by A.P. Riascos and Jose L. Mateos.
2. 2. Table of content dynamics Formalism networks of on 2. diffusion process! +! normal random walks fractional diffusion! +! long-range dynamics 1. General for networks terminologies ! Example on a 1: tree network! Example on a 2: ring network! Fractional return! probability
3. 3. Description of networks
4. 4. diffusion process and normal random walks Stochastic approach Deterministic approach structure! of network Adjacency ! matrix A Laplacian ! matrix L Transitian ! matrix W
5. 5. how to make the dynamics fractional? non-fractional fractional Stochastic approach Deterministic approach
6. 6. Example 1: network on a tree structure! of network Adjacency ! matrix A Laplacian ! matrix L Transitian ! matrix W Fractional! Laplacian Observation: long-range dynamics/ global dynamics in networks
7. 7. Example 2: network on a ring (periodic) geodesic distance the Levy! measure of! a stable ! process !
8. 8. Average fractional return probability versus topology of the network Definition asymptotic power law a ring a tree a scale-free network! of the Brabasi-Albert type the return probability ! depends on the shapes ! of the network!
9. 9. Global time also depends on shapes of networks efficiency to explore the network Questions:! 1. is the emergence of Levy flight shape-dependent?! 2. 'tempered' fractional dynamics on networks?! 3. how to introduce 'spectral methods' onto networks?! 4. how do probability quantities depend on the structure of networks?