Preliminary Course.
Plant and crop Models
Typology (3)
Computational and Mathematical Models
In the application of Plant Sciences, explanatory models are usually implemented on computers.
Those implementations may be the implementation of simple mathematical formulae, or be based on the simulation of interactions, simulated from rules or behaviour patterns.
This distinction is important, since model expressions, definitions and potential applications are related to it.
In the latter case, we speak about computational models, in the former case we speak about mathematical models.
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Computational models
A computational model is a formal model in computational science that requires extensive computational resources to study the behaviour of a complex system by computer simulation.
The system under study is often a complex nonlinear system for which simple, intuitive analytical solutions are not readily available.
Rather than deriving a mathematical analytical solution to the problem, experimentation with the model is done by adjusting the parameters of the system in the computer, and studying the differences in the outcome of the experiments.
The operation theories of the model can be derived/deduced from these computational experiments.
Mathematical models
A mathematical model is a description of a system using mathematical concepts and language.
The process of developing a mathematical model is termed mathematical modelling.
A model may help to explain a system and to study the effects of different components, and to make predictions about behaviour.
Mathematical models can take many forms, including but not limited to dynamic systems, statistical models, differential equations, or game theory models.
These and other types of models can overlap, with a given model involving a variety of abstract structures.
In many cases, the quality of a scientific field depends on how well the mathematical models developed on the theoretical side agree with the results of repeatable experiments.