The Study Of Food Chain Model With B-D Functional Response

Chemostat model is one of the most significant models in Mathematical biology. The Chemostat is an important device used for growing micro-organisms in a continuous cultured environment, and a medium of great importance between principles and applications. It has been widely applied to the study of the increase in different populations of micro-organisms and their interactive law. In addition, it has also been applied to the management and prediction of the ecology system, especially the marine ecology, and the control of the environment pollution. The main contents and results in this dissertation are as follows:i) A food chain model with B-D functional response in time varying environment is studied. The existence of semi-strival solutions is got and that the stability of the solutions proofed via Floquet theory. The existence of periodic solutions is determined by the simple aigenvalues brifurcation theory. At last, the numerical simulation for the model is obtained by matlab soft, further more, the results of numerical simulation correspond to the theoretics analysises.ii) Multiple food chain model with partial differential equations was established to simulate various ecological forms with both competition and predator-prey in the course of microorganisms' continuous growth in the nature. Predator-prey-related B-D functional response was selected as growth function based on characteristics of the multiple food chain. Existence conditions of semi-trivial equilibrium solutions with principal eigenvalue theory of partial difference operator and comparison principle were analyzed. The existence of positive equilibrium solutions was obtained using fixed point theory in the cone. Theoretical analyses indicate that the coexistence of all species are possible.