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Full-Text Articles in Environmental Microbiology and Microbial Ecology
Contraction Analysis Of Functional Competitive Lotka-Volterra Systems: Understanding Competition Between Modified Bacteria And Plasmodium Within Mosquitoes., Nickolas Goncharenko
Contraction Analysis Of Functional Competitive Lotka-Volterra Systems: Understanding Competition Between Modified Bacteria And Plasmodium Within Mosquitoes., Nickolas Goncharenko
Electronic Thesis and Dissertation Repository
We propose and analyze an extension to the classic Competitive Lotka-Volterra (CLV) model. The goal is to model competition between species, with a response from the environment. This response is a function of the population of all species and can represent numerous physical phenomena including resource limitation and immune response of a host due to infection. We name this new system a Functional Competitive Lotka-Volterra (FCLV) model. We mainly use the construction of contraction metrics, to determine global properties of the model. We use this result to analyze the competition between Plasmodium sp. and genetically engineered bacteria within the midgut …
Modelling Non-Linear Functional Responses In Competitive Biological Systems., Nickolas Goncharenko
Modelling Non-Linear Functional Responses In Competitive Biological Systems., Nickolas Goncharenko
Western Research Forum
One of the most versatile and well understood models in mathematical biology is the Competitive Lotka Volterra (CLV) model, which describes the behaviour of any number of exclusively competitive species (that is each species competes directly with every other species). Despite it's success in describing many phenomenon in biology, chemistry and physics the CLV model cannot describe any non-linear environmental effects (including resource limitation and immune response of a host due to infection). The reason for this is the theory monotone dynamical systems, which was codeveloped with the CLV model, does not apply when this non-linear effect is introduced. For …