BIFURCATION STRUCTURE OF A 3-SPECIES FOOD-CHAIN MODEL

A three-species food chain model utilizing type II functional response s and allometric relationships is analyzed mathematically. A reduction of the two-dimensional nullsurfaces to a set of one-dimensional curve s allows for an intuitive understanding of the equilibria structure. W ith the reduction in hand, we then perform a local bifurcation analysi s around an organizing center and categorize the entire parameter spac e into twelve different regions of dynamic behaviour. These regions in parameter space are characterized by an extremely rich set of dynamic al behaviours, including multiple domains of attraction, quasi-periodi city, chaos, homoclinic events, and transient chaos. From this mathema tical analysis it is possible to qualify the type of population dynami cs under any given parameter set. (C) 1995 Academic Press, Inc.