The Lotka-Volterra Predator-Prey Equations

One may find out the application‎ ‎of mathematics in the areas of ecology‎, ‎biology‎, ‎environmental‎ ‎sciences etc‎. ‎Mathematics is particulary used in the problem of‎ ‎predator-prey known as lotka-Volterra predator-prey  equations.‎ ‎Indeed‎, ‎differential equations is employed very much in many areas‎ ‎of other sciences‎. ‎However‎, ‎most of natural problems involve some‎ ‎unknown functions‎. ‎In this paper‎, ‎an environmental case‎ ‎containing two related populations of prey and predator species is‎ ‎studied‎. ‎As the classic Lotka-Volterra assumptions are‎ ‎unrealistic‎, ‎it is assumed that there is logistic behavior for‎ ‎both existing species‎. ‎We see that two populations influence the‎ size of each other.‎