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The dynamics of exploitation in ensembles of source and sink

Friedrich, T. (2012): The dynamics of exploitation in ensembles of source and sink.

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The ensemble is a new entity on a higher level of complexity composed of source and sink. When substrate is transferred from source to sink within the transfer space non-linearity may be observable. Saturating production functions of source and sink in combination with linear cost functions may generate superadditivity and subadditivity in the productivity of the ensemble. The combined and interdependent productivity of the ensemble forms a surface similar to the Cobb-Douglas surface in a reaction chain where the source produces a product that will be used by the sink to produce a different product. Source and sink form a harmonic ensemble. When source and sink use the same substrate there will be competition. The surface is only present in active parts of the ensemble. Both parties may have different saturating production functions, different linear cost functions and different amounts of substrates in their compartment. If substrate is now transferred following the concentration gradient in harmony or through brute force or information (education) superadditivity or subadditivity may appear. The surface within the transfer space is now in some regions above or below the Cobb-Douglas surface. When substrate is repeatedly transferred from source to sink the actual productivity of the ensemble moves along the surface to a stable point or one party is lost and the ensemble is destroyed. This movement is the dynamic aspect of the ensemble. The benefit of source and sink and the cost can be interpreted as three-dimensional, non-linear coordinates of the ensemble appearing within the transfer space.

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