We will generalize the Perron-Probenius theorem for square matrices to nonlinear maps, adding the condition of subadditivity (called (C3)) in the sequel to the usual conditions. In the terminology of economics, we ate concerned with the nonlinear Leontief model. One of the main results is the canonical decomposition theorem. To accomplish this result, ir is also necessary to modify slightly the definition of indecomposability in the earlier works.
We ate concerned with the cyclic predator-prey systems of Volterra-Lotka type where the 1st species feeds on the 2nd, the 2nd on the 3rd, 9 -., the n-th on the 1st cyclically and each species has the self-limiting terms. The purpose of this paper is to give a necessary and sufficient condition for the parameters of this type of systems so that every nonnegative solution remains bounded as the time passes.
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