АНАЛИТИЧЕСКИЙ И СИМУЛЯЦИОННЫЙ ПОДХОДЫ К ИЗУЧЕНИЮ ИНТЕГРАЛЬНОГО УРАВНЕНИЯ, ВОЗНИКАЮЩЕГО ПОСЛЕ ЗАМЫКАНИЯ ТРЕТЬЕЙ СТЕПЕНИ
This article explores nonlinear integral equation system that appears in the biological model of spatial stochastic population dynamics by U. Dieckmann and R. Law. We introduce the model and explain the reasoning behind using spatial moments within this model. We show derivation of nonlinear integral equation for equilibrium state after performing third degree closure on infinite system of linear integro-differential equations describing spatial moment dynamics. The nonlinear equation is transformed to the representation that allows effective application of a numerical method based on Neumann series. We developed a numerical method solving the resulting nonlinear integral equation and provided an example of using this method and working with this modeling. We found that there exists nontrivial solution with positive Poisson death rate, which significantly distinguishes the nonlinear equation from its previously researched linear counterparts.