Uncertain Linear Stationary Model of Population Density in a Bounded Habitat

The purpose of this article is to identify an uncertain linear time-invariant (LTI) model of the spatial distribution of a specimen over 1-D habitual space. Population density is described by a nonlinear reaction-diffusion partial differential equation (PDE) following the population dynamics theory. The nonlinear PDE is approximated with a linear parameter varying state-space model from the 120th order with two inputs and 100 outputs, which describe the spatial distribution where the manipulated variable in the model is the length of the habitat. A random excitation signal is applied corresponding to expansion or contraction of the habitual space to assess the dynamical response of the population density. The collected data are used to estimate 100 Box and Jenkins (BJ) models, which describe the reaction of population density across the habitat. Then, a single uncertain LTI model is identified from the magnitude frequency response of the BJ models to cover all of them.