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Migration on networks and its stability consequences
Author(s) -
Alekseeva Elena I.,
Kirzhner Valery M.
Publication year - 1994
Publication title -
system dynamics review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 57
eISSN - 1099-1727
pISSN - 0883-7066
DOI - 10.1002/sdr.4260100105
Subject(s) - pointwise , stability (learning theory) , computer science , diffusion , pointwise convergence , mathematics , physics , mathematical analysis , machine learning , approx , thermodynamics , operating system
This article reviews the authors' studies on the behavior of materially coupled dynamic systems. It discusses models of a network of a finite number of localized (pointwise) systems connected through an interaction structure involving migration, diffusion, or other forms of material exchange. On the basis of an analytical criterion for the stabilizing or destabilizing influence of the connecting structure, a classification of possible types of such structures and of the pointwise systems themselves is given. A model of a multicentric immunodependent tumor is analyzed. Tumor nodules and white blood cells are regarded as localized systems and migrating agents, respectively. We illustrate the possibility of predicting the behavior of the whole multicentric system from the internal parameters in each nodule and discuss the possibility of regulating multicentric tumor growth by controlling the intensity of migration of cells in the body.