an analysis on the lotka-volterra food chain model: stability

The food chain refers to a natural system by which energy is transmitted from one organism to another. in fact, a food chain consists of producers, consumers and decomposition. presence of complex food web increase the stability of the ecosystem. classical food chain theory arises from lotka-volterra model. in the present paper, the dynamics behavior of three level food chain is studied. a system of 3 nonlinear odes for interaction modeling of three-species food chain where intraspcies competition exists indeed is studied. the first population is the prey for the second which is prey for the third one. it is clear that it is the top of food pyramid. the techniques of linearization and first integral are employed.