A kinetic theory approach to modeling prey–predator ecosystems with expertise levels: analysis, simulations and stability considerations

Abstract

In this paper a kinetic modeling approach for an ecological system is proposed, based on the prey–predator structure in terms of individuals experience. Specifically, a system of nonlinear kinetic equations is formulated using standard tools. Both conservative and nonconservative events are considered since proliferative/destructive rates and an external force field occur. These results are compared to the ones of the classical theory of dynamical system to show their consistency. In addition to a first local analytical result, some numerical simulations are performed. The results thus obtained ensure that the kinetic model behaves in a way consistent with other similar ecological models formulated by dynamical systems, involving ordinary differential equations with lumped dependent variables. For each simulation, stationary solutions are shown. Moreover, oscillations appear for some values of the parameters of the ecological system, and this suggests that bifurcations may appear.