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Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
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 …
Real Solution Of Dae And Pdae System, Zahra Mohammadi, Greg Reid
Real Solution Of Dae And Pdae System, Zahra Mohammadi, Greg Reid
Western Research Forum
General systems of differential equations don't have restrictions on the number or type of equations. For example, they can be over or under-determined, and also contain algebraic constraints (e.g. algebraic equations such as in Differential-Algebraic equations (DAE) and Partial differential algebraic equations (PDAE). Increasingly such general systems arise from mathematical modeling of engineering and science problems such as in multibody mechanics, electrical circuit design, optimal control, chemical kinetics and chemical control systems. In most applications, only real solutions are of interest, rather than complex-valued solutions. Much progress has been made in exact differential elimination methods, which enable characterization of all …