On the entropy of the predator-prey model

In this paper a characterization of the new concept of entropy of a dynamic system is discussed. A new graphical approach is used to quickly get a feeling of the local nonlinearity of planar dynamical systems. A user-friendly tool in MATLAB/Simulink has been designed in order to automatize computation of the entropy and easy visualization as color maps. The proposed approach is used to analyze the well-known predator-prey Lotka-Volterra model. By using the simplified assumption of infinite carrying capacity for the preys, different cases have been tested, namely those exhibiting more variability in predators, more variability in preys or equivalent variation between the two species. The results show that the entropy of a system is a concept fairly different from the shape of the trajectories of the system in the phase plane. Indeed, while the behavior of the relative variability of predators or prey depend on their behavior in the absence of the other species, the entropy steadily increases with the increase in variability of the number of predators, a concept that makes sense from the biological point of view. Moreover, the results do not change very much if a finite carrying capacity for the prey is considered, the main difference being a reduction of entropy due a lower variability of the two populations.