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Abstract:
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Using the PACE software introduced at the SAMSI workshop last fall, I am examining a feature of selection between nonlinear vs linear timevarying coef. models used in biological applications. More specifically, I am considering one dimensional Gompertzian growth model that was used in collaboration with a Food Science project and a two dimensional neuronal model, Fitzhugh-Nagumo, used for the voltage potential across a nerve membrane. It is difficult with only one initial condition value, even if replicated many times, to distinguish nonlinear vs linear timevarying noisy ordinary differential equation models. This research looks at how other initial conditions can be chosen and at what distance in the state variable and in the parameter space to statistically distinguish the types of models by Akaike Information Criterion. When noise is introduced in the differential equation rather than as observation error, the effects of correlated and non constant variance must also be incorporated. Using the phase plane for the two dimensional model is a useful diagnostic tool.
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