Variational Principles and Conservation Conditions in Volterra's Ecology and in Urban Relative Dynamics

Dendrinos, D.S. & Sonis, M. (1984). Variational Principles and Conservation Conditions in Volterra's Ecology and in Urban Relative Dynamics. IIASA Collaborative Paper. IIASA, Laxenburg, Austria: CP-84-049

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Abstract

Contribution to the Metropolitan Study: 14 -- From an analytical viewpoint, Volterra's variational principles and their associated integrands in single and multiple species interaction under absolute growth conditions in the field of mathematical ecology are reconsidered and simplified. They are then compared with the conservation conditions found appropriate to hold in a class of dynamic problems of relative growth in urban analysis. The comparison assists in interpreting the integrands of geographical (spatial) associations as a "stationary effort fitness function" associated with a cumulative entropy measure of the relative urban dynamic spatial distributions.

From a substantive viewpoint, the paper shows the theoretical conditions, which would result in all spatial activity to be concentrated into a single point, so that inferences can be made regarding the conditions under which the activity will disperse. It also demonstrates that assuming a particular problem formulation, in this case a relative dynamic framework in an inactive environment, will result in obtaining spatial competitive exclusion. This is demonstrated in a parsimonious manner.

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