Complex Non-Unique Dynamics in Simple Ecological Interactions
We report here a host-macroparasite interaction in which several types of attractors may coexist. A proportion of host population is immune to the parasite. The basic attractors observed in this two-species interaction include point equilibria, 2-, 3-, 6-, 12-, and 8-cycles, quasicycles, and 3-piece and 6-piece chaotic attractors. The attractors depend on the initial population levels as well as on the proportion of immune hosts. Changes in the proportion of immune hosts may either stabilize or destabilize the interaction. The non-uniqueness of the attractors implies that the bifurcation diagrams, or the routes to chaos, may also not be unique, but may depend on the specific initial population level chosen. The basins of attraction, defining the initial conditions leading to a certain type of an attractor, may be fractal sets, even in the case of two non-chaotic attractors. The fractal property observed is the pattern of self-similarity. It follows that sensitivity of the trajectory with respect to the initial condition can be observed in the absence of chaos in the dynamics.
Proceedings of the Royal Society of London Series B
- Pub Date:
- August 1996