Mathematical Modelling Techniques

Models are concepts of reality

Mathematical Modelling is the mathematical technique of getting concepts mathematical which you only have a qualitative representation of linguistic description, a video recording, or any other possibility and striving a quantitative description where one should test against measurements of the phenomenon.

When delving into the analysis and quantitative prediction of ecosystem dynamics, the application of Mathematical modelling techniques becomes imperative. This approach mirrors that employed in disciplines such as quantum mechanics, molecular biology, and biophysics. It's important not to be captivated solely by the allure of mathematical models; these models lack inherent character or affiliation. Both physics and mathematics should be perceived as potent tools, serving as aids rather than absolute sources of knowledge.

Describe

Describe the real-world problem. Identify and understand the practical aspects of the situation.

Specify

Specify the mathematical problem. Frame the real-world scenario as an appropriate, related mathematical question(s).

Communicate

Communicate clearly and fully your suggestions to address the real-world problem.

Report and interpret

Report and interpret the solution of the mathematical model.

Solve

Solve the mathematics using software to get the solution.

Interpret

Interpret the solution. Consider mathematical results in terms of their real-world meanings.

Formulate

Formulate the mathematical model. Make simplifying assumptions, choose variables, estimate magnitudes of inputs, justify decisions made.

Evaluate

Evaluate the model. Make a judgment as to the adequacy of the solution to the original question(s). Modify the model as necessary and repeat the cycle until an adequate solution has been found.

Different Model used for Mathematical modelling techniques

Deterministic vs. Stochastic models

Deterministic models have no components that are inherently uncertain, i.e., no parameters in the model are characterized by probability distributions, as opposed to

Qualitative vs. Quantitative Models

Qualitative models lead to a detailed, numerical prediction about responses, whereas qualitative models lead to general descriptions about the responses

Static vs. Dynamic Models

Static models are at an equilibrium or steady state, as opposed to dynamic models which change with respect to time.