Integral population models
by
Shinji Yamamoto
Department of Mathematics and Statistics, University of Canterbury

ODEs have been usually used to describe population models and will continue to be so in the future. This is because there is a vast quantity of matters which can be applied to ODEs. However, it is true that there are a lot of phenomena in the nature which ODEs cannot describe and this is also true for population dynamics. (For instance where there are time delays, continuous age distributions, history of the population, etc). So, functional ODEs (Delay-differential equations or Integro-differential equations) and PDEs have been introduced more recently to describe the phenomena which we cannot model by just using ODEs, even if they are more difficult to be analyse than ODEs. Here, we have recently constructed another type of population model, which is an integral equation model. This is a rather unusual type of population model. In this talk, I will discuss the basic concepts, the formulation of the model and its local stability.

Date received: June 23, 1999