Subtle global bifurcation with dramatic ecological consequences in a simple population model

Numerous situations exist in which a consumer uses two different kinds of resources, one fixed, the other renewable, e.g., nesting resources and food resources. With an elementary modification of the basic Lotka–Volterra consumer resource equations, we investigate the population dynamics of a consumer dependent on two resources, one fixed, the other renewable. Emerging from this structure is a situation of alternative attractors that remain qualitatively robust over a significant range of parameter values. However, a dramatic change in basins of attraction is induced by very small changes in parameters due to a global bifurcation. Noteworthy is the fact that the qualitative nature of the alternative equilibria remains constant but the dramatic change in the basins does not arise from subtle differences in initial conditions. Rather, there is a major restructuring of the vector field such that a permanent change involving large sets of initial conditions results from very small changes in parameters.