โ Scribed by P. Cull
No coin nor oath required. For personal study only.
In general, local stability does not imply global stability. We show that this is true even if one only considers population models.
We show that a population model is globally stable if and only if it has no cycle of period 2. We also derive easy to test sufficient conditions for global stability. We demonstrate that these sufficient conditions are useful by showing that for a number of population models from the literature, local and global stability coincide.
We suggest that the models from the literature are in some sense "simple", and that this simplicity causes local and global stability to coincide. for global stability of population models. We will show that a population model is globally stable if and only if the model has no cycles of period 2. Unfortunately, this necessary and sufficient condition may not be easy to test for many specific models. We address this difficulty by deriving some sufficient conditions which are easier to test. Then we show how these sufficient conditions can be used to prove the equivalence of local and global stability for various models from the literature. We include in our demonstration the models used by Nobile et al. (1982). Some of the results of this paper have appeared in Cull (1981).
๐ SIMILAR VOLUMES
Local stability seems to imply global stability for population models. To investigate this claim, we formally define a population model. This definition seems to include the onedimensional discrete models now in use. We derive a necessary and sufficient condition for the global stability of our defi
The dynamical theory of food webs has been based typically on local stability analysis. The relevance of local stability to food web properties has been questioned because local stability holds only in the immediate vicinity of the equilibrium and provides no information about the size of the basin