Effects of carrying capacity and delay on the dynamics of Lotka–Volterra system: Mathematical, numerical and microcontroller simulation

Abstract

This work carries out an analytical, numerical and microcontroller simulation of the Lotka-Volterra model. The main objective is to show the importance of analyzing dynamical behaviour of systems through a microcontroller. To achieve this, two main aspects are pointed up: the effect of the carrying capacity and delay. Concerning the carrying capacity, increasing its value in the absence of delay brings predator and prey densities closer, while the system remains stable. As for the second aspect, the delay is considered. An analytical study is made and allows to circumscribe the zones of stability and instability according to the delay for the value of the fixed the carrying capacity. Numerical and microcontroller simulations are made and the results obtained have the same identical behaviours.