Discrete Dynamical Systems: With Applications in Biology

Mathematical modeling of population dynamics has been attracted by many researchers over the last few decades. Specially, exponential difference equations have been used to model the interactions between different kind of population dynamics. Among these population models, Host-Parasitoid interactions play an important role in the ecosystem. A parasitoid is an organism that feeds another organism. The host is the organism which the parasitoid feeds. We have two different approaches to model these interactions, discrete and continuous. However, the discrete time models governed by difference equations are more realistic, rational and applicable rather than the continuous systems specially when the populations follow the non-overlapping generations. A well-known example of this non-overlapping is Insects which adults lay eggs in spring/summer and then die. The eggs hatch into larvae which eat and grow and then in the winter they fall in a pupal stage. The adults appear from the pupae in spring. Moreover, discrete models can present much more dynamical behaviors compared to the continuous-time model.