Stability analysis of the solution to a system of nonlinear integral equations arising in a logistic dynamics model

In this paper, we analyze a system of nonlinear integral equations resulting from the three-parameter closure of the third spatial moments in the logistic dynamics model of U. Dieckmann and R. Law in the multi-species case. Specifically, the conditions under which the solution of this system is stable with respect to the closure parameters are investigated. To do this, the initial system of equations is represented as a single operator equation in a special Banach space, after which the generalized fixed point principle is applied.