eTEXT

Fractional Dynamics on Networks and Lattices

By: Thomas Michelitsch, Alejandro Perez Riascos, Bernard Collet, Andrzej Nowakowski, Franck Nicolleau

Write A Review

eText | 10 April 2019 | Edition Number 1

At a Glance

Format
ePUB

eText

$260.69

or 4 interest-free payments of $65.17 with

or

Instant online reading in your Booktopia eTextbook Library *

Read online on

Desktop

Tablet

Mobile

Not downloadable to your eReader or an app

This book analyzes stochastic processes on networks and regular structures such as lattices by employing the Markovian random walk approach.

Part 1 is devoted to the study of local and non-local random walks. It shows how non-local random walk strategies can be defined by functions of the Laplacian matrix that maintain the stochasticity of the transition probabilities. A major result is that only two types of functions are admissible: type (i) functions generate asymptotically local walks with the emergence of Brownian motion, whereas type (ii) functions generate asymptotically scale-free non-local "fractional" walks with the emergence of Levy flights.

In Part 2, fractional dynamics and Levy flight behavior are analyzed thoroughly, and a generalization of Polya's classical recurrence theorem is developed for fractional walks. The authors analyze primary fractional walk characteristics such as the mean occupation time, the mean first passage time, the fractal scaling of the set of distinct nodes visited, etc. The results show the improved search capacities of fractional dynamics on networks.