Permanency and Asymptotic Behavior of The Generalized Lotka-Volterra Food Chain System

In the present paper a generalized Lotka-Volterra food chain sys- tem has been studied and also its dynamic behavior such as locally asymptotic stability has been analyzed in case of existing inter- species competition. Furthermore, it has been shown that the said system is permanent (in the sense of boundedness and uniformly persistent). Finally, it is proved that the nontrivial equilibrium point of the above system is locally asymptotically stable.