Bifurcations

The transition from the non-being of a state into the existence of it, supposing that this state contains no quality which previously existed in the phenomenon, is a fact of itself demanding inquiry.

— IMMANUEL KANT (.Critique of Pure Reason)

In Chapter 2 we developed a model for the dynamics of a population with three life-cycle components: a larval stage, a pupal stage, and an adult stage. We parameterized and validated this model using time series of data for an insect species, namely, the flour beetle species T. castaneum. In this chapter we turn our attention to a study based on some predictions of this parameterized model. As we will see, the model predicts a specific sequence of bifurcations in dynamic behavior as the adult death rate ¡ia of the beetles is changed from its value estimated in Chapter 2. This bifurcation sequence, it turns out, does not involve chaos. Nonetheless, it does provide an excellent experimental opportunity to document the occurrence of model predicted bifurcations in the dynamics of a real biological population. Such an experimental project, if successful, would have two important consequences for our long term goals. First, it would represent an additional validation of the LPA model in the sense that it would substantiate the model's ability to predict dynamics that can be documented by controlled laboratory experiments. Second, this preliminary bifurcation experiment would serve as the starting point for other projects that document model predicted sequences of more complicated bifurcations and, in particular, a sequence of bifurcations involving chaos.

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