2 research outputs found
Memory and mutualism in species sustainability: a time-fractional Lotka-Volterra model with harvesting
We first present a predator-prey model for two species and then extend the
model to three species where the two predator species engage in mutualistic
predation. Constant effort harvesting and the impact of by-catch issue are also
incorporated. Necessary sufficient conditions for the existence and stability
of positive equilibrium points are examined. It is shown that harvesting is
sustainable, and the memory concept of the fractional derivative damps out
oscillations in the population numbers so that the system as a whole settles on
an equilibrium quicker than it would with integer time derivatives. Finally,
some possible physical explanations are given for the obtained results. It is
shown that the stability requires the memory concept in the model