System identification: theory for the user
System identification: theory for the user
Fractals everywhere
Fractal Image Compression and Recurrent Iterated Function Systems
IEEE Computer Graphics and Applications
Mathematical modelling and parameter estimation of the Serra da Mesa basin
Mathematical and Computer Modelling: An International Journal
Mathematics and Computers in Simulation
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We propose a 2D ecological model of phytoplankton dynamics accounting for the distribution and the evolution of algae in a large basin located in the Amazonian region. The model is described by a set of reaction-drift-diffusion equations and is driven by several exogenous inputs, such as wind velocity and direction, water temperature and solar radiation. Due to the roughness of the domain, a preliminary boundary extraction with a curvelet algorithm is performed. Then, the model is simulated in an approximated domain, where the contour has been reconstructed by estimating a set of Recurrent Fractal Interpolation Functions, aimed at preserving its fractal structure. Simulations are combined with time and space chlorophyll-a data in order to estimate the parameters of the model. The proposed algorithm is based on an iterative two-step identification procedure, where reaction parameters are recovered first and then used for estimating diffusion and transport parameters. Comparison results at different accuracy approximations and before and after the algorithm implementation are presented and discussed.