MATERIAL RECYCLING IN A CLOSED AQUATIC ECOSYSTEM. Ⅱ. BIFURCATION ANALYSIS OF A SIMPLE FOOD-CHAIN MODEL

摘要

The present paper deals with the bifurcation analysis of a simple food chain model consisting of components like detritus, nutrients, microorganisms, phytoplankton and zoo-plankton in an aquatic environment. The food chain model is described by a system of differential equations. If the length of the food chain (LFCH) is equal to 3 or 4, then an asymptotically stable equilibrium exists. For LFCH = 5 or 6 the non-trivial equilibrium is unstable and the food-chain model has periodic orbits.