Chapter

Spatial–temporal extensions

Eric Renshaw

in Stochastic Population Processes

Published in print February 2011 | ISBN: 9780199575312
Published online September 2011 | e-ISBN: 9780191728778 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199575312.003.0010
Spatial–temporal extensions

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Although the Turing model and the Markov chain process are both ideal for studying systems which involve spatial interaction between adjacent sites, in practice interaction may occur across much larger spatial levels. Moreover, there is no reason why locations have to lie on a lattice structure, which has been our presumption so far in order to enable some degree of mathematical tractability. This chapter presents two extensions to earlier spatial analyses. The first introduces the concept of long-range dependence, whilst the second examines processes which develop over real, rather than discrete, space.

Keywords: spatial analyses; long-range dependence; real space; Turing model; Markov chain processes

Chapter.  28857 words.  Illustrated.

Subjects: Applied Mathematics

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