A model of hierarchical ecosystems with utility efficiency of mass and its stability

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Abstract
A model of hierarchical ecosystems with utility efficiency of mass, which is an extension of Nisbet and Gumey's model, is proposed and its local and global stability are discussed. In particular, the relation between stability and utility efficiency of mass is studied. As concerns local stability, positive equilibrium is always asymptotically stable whatever the rates of utility efficiency of mass are. This means that mass cycling enables the ecosystem to stabilize whatever the rates of utility efficiency of mass are. With regard to global stability, the ecosystem moves asymptotically to an equilibrium which shows the most prosperous state (existence of most levels) in all the equilibria.

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