2001, Volume 4, Number 3, pp.264-279

The content of this lecture is three-folded. First of all, a new branch of the non-linear discrete dynamics are presented: the Discrete Relative m-population/n-location Socio-Spatial Dynamics elaborated by D.S. Dendrinos and M.Sonis starting in 1984 and summarized in a book: D.S. Dendrinos, M. Sonis, Chaos and Socio-Spatial Dynamics, Springer Verlag Series of Applied Mathematics, vol. 86, 1990. Further, the Entropy Maximization principle for their derivation is presented. Third, the elements of control of bifurcations are elaborated on the basis of the classical Routhian formalism. The control of bifurcations can be achieved by travels of equilibria in the space of orbits of the iteration processes. The crossing the boundaries of the stability domain reveals the plethora of possible ways from stability, periodicity, the Arnols mode-locking tongues and quasi-periodicity to chaos. At the end the algorithm of the control of bifurcations is used for the detail analysis of two particular models: the log-linear model of the labor-capital core-periphery discrete relative dynamics and the log-log-linear model of the one population/three location discrete relative dynamics.
Key words: socio-spatial dynamics, nonlinear discrete dynamics, bifurcation, chaos, Entropy Maximization principle

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