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.‎