Complex Non-Unique Dynamics in a Host-Parasitoid Model Incorporating Clumping Effect

Abstract

In this paper, Computer simulation is used to study the influence of clumping effect on the dynamic complexities of a discrete-time host-parasitoid model. We report here parasitoid aggregation may be a strong stabilizing or destabilizing factor. Using computer simulation, many forms of complex dynamic are observed, including Hopf bifurcation reversal, period-halving, attractor crises, chaotic bands with narrow or wide periodic windows, intermittent chaos, and supertransient behavior. Several types of attractors, e.g. point equilibrium vs. chaotic, periodic vs. quasiperiodic and quasiperiodic vs. chaotic attractors, may coexist in the same mapping. This non-uniqueness also indicates that the bifurcation diagrams, or the routes to chaos, depend on initial conditions and are therefore non-unique. The basins of attraction, defining the initial conditions leading to a certain attractor, may be fractal set. The fractal property observed is the pattern of self-similarity. The numerical results indicate that computer simulation is a useful method of investigating complex dynamic systems. We also conclude that non-unique dynamic, associated with the extremely complex structure of the basin boundaries, can have a profound effect on our understanding of the dynamical processes of nature.