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Full-Text Articles in Non-linear Dynamics
The Sir Model When S(T) Is A Multi-Exponential Function., Teshome Mogessie Balkew
The Sir Model When S(T) Is A Multi-Exponential Function., Teshome Mogessie Balkew
Electronic Theses and Dissertations
The SIR can be expressed either as a system of nonlinear ordinary differential equations or as a nonlinear Volterra integral equation. In general, neither of these can be solved in closed form. In this thesis, it is shown that if we assume S(t) is a finite multi-exponential, i.e. function of the form S(t) = a+ ∑nk=1 rke-σkt or a logistic function which is an infinite-multi-exponential, i.e. function of the form S(t) = c + a/b+ewt, then …
Non-Classical Symmetry Solutions To The Fitzhugh Nagumo Equation., Arash Mehraban
Non-Classical Symmetry Solutions To The Fitzhugh Nagumo Equation., Arash Mehraban
Electronic Theses and Dissertations
In Reaction-Diffusion systems, some parameters can influence the behavior of other parameters in that system. Thus reaction diffusion equations are often used to model the behavior of biological phenomena. The Fitzhugh Nagumo partial differential equation is a reaction diffusion equation that arises both in population genetics and in modeling the transmission of action potentials in the nervous system. In this paper we are interested in finding solutions to this equation. Using Lie groups in particular, we would like to find symmetries of the Fitzhugh Nagumo equation that reduce this non-linear PDE to an Ordinary Differential Equation. In order to accomplish …