생물 종의 개체 수 변화를 기술하는 수학적 모델의 확산현상 표현에 대한 역사적 고찰

A Historical Study on the Representations of Diffusion Phenomena in Mathematical Models for Population Changes of Biological Species

In mathematical population ecology which is an academic field that studies how populations of biological species change as times flows at specific locations in their habitats, PDE models have been studied in many aspects and found to have different properties from the classical ODE models. And different approaches to PDE type models in mathematical biology are still being tried currently. This article investigate various forms to express diffusion effects and review the history of PDE models involving diffusion terms in mathematical ecology. Semi-linear systems representing the spatial movements of each individual as random simple diffusion and quasi-linear systems describing more complex diffusions reflecting interspecific interactions are studied. Also it introduce a few of important problems to be solved in this field.