Instabilities in single-species and host-parasite systems: Period-doubling bifurcations and chaos

Of concern in the paper is the stability of populations which change their size according to the Hassell growth function, not only in isolation, but also under external effects such as migration. The mathematical model developed is applied to a host-parasite system and the dynamics of the resulting system are studied analytically. The numerical simulations demonstrate the inherent instabilities in the single-species system, which manifest itself in the form of period-doubling bifurcations and chaos. It is found that the effect of migration is to suppress such an unstable behaviour.