A nonconservative kinetic framework with logistic growth for modeling the coexistence in a multi-species ecological system

TL;DR

This paper develops a nonconservative kinetic model with external forces to describe multi-species ecological systems, analyzing stability and bifurcations, and providing numerical simulations of prey-predator interactions.

Contribution

It introduces a novel nonconservative kinetic framework with external forces for ecological modeling, extending traditional kinetic theories to better capture complex interactions.

Findings

Stability analysis of coexistence equilibrium

Identification of Hopf bifurcations in the system

Numerical simulations illustrating ecological dynamics

Abstract

Kinetic theory frameworks are widely used for modeling stochastic interacting systems, where the evolution primarily depends on binary interactions. Recently, in this framework the action of the external force field has been introduction in order to gain a more realistic picture of some phenomena. In this paper, we introduce nonconservative kinetic equations where a particular shape external force field acts on the overall system. Then, this framework is used in an ecological context for modeling the evolution of a system composed of two species interacting with a prey-predator mechanism. The linear stability analysis concerned with the coexistence equilibrium point is provided, and a case where a Hopf bifurcations occurs is discussed. Finally, some relevant scenarios are numerically simulated.