Build a dynamical system, Build a dynamical system for your

Build a dynamical system

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Reference no: EM133772074

Course Project

Throughout the duration of the course the learner will develop and analyze a mathematical model using the techniques presented in the course. Read all the directions and examples of every topic before beginning this project. The examples are meant to suggest possible approaches, but feel free to explore. Also, the examples do not include any of the mathematical analysis that is required to complete the project. The techniques will be gradually introduced during the coursework.

Topic 1
Select a topic for the project and in particular, the quantity that will be modeled. The choice should be based on personal preference, but it should be thoroughly researched. The use of scholarly papers as inspiration is encouraged.
Post your choice with your reasoning via the Discussion Forum in the LMS. Provide at least one reference for the material that inspired the choice.

Topic 2
Build a dynamical system for your chosen topic consisting of a first order non-linear ordinary differential equation (ode) and the suitable parameters as well as the parameters' value choices. Justify each choice with a substantive argument and provide references where appropriate. In addition, identify and classify the steady states for the given model as well as create a graph (using MATLAB) containing the vector field.

Topic 3
Analyze the model dependence on its parameters. The study should include bifurcation point(s) analysis, classification, and bifurcation diagrams, as needed.

Prepare an executive summary report of all of your project work to this point. Your summary should include the following:
• A one dimensional model with a clear description of its variables, parameter and terms
• Stability and Bifurcation analysis
• Conclusions
Your analysis should include all of the relevant calculations and graphs.

Topic 4
Add a new quantity to be modeled. Use this second first order nonlinear differential equation to create a 2-D model. This choice should follow logically from the topic of the project and the format of the second ODE. Its parameters should be described and justified, providing references where appropriate. The equations in the new 2-D system should be coupled, meaning that at least one of the two unknown quantities should be present on both of the differential equations of the system. Adding a new "player" to the model will likely change the original ode as well.

Topic 5
Analyze the stability of the newly created two-dimensional system using appropriate choices of the parameters of the system. This analysis will contain fixed points, fixed point classification linearization, stable and unstable manifolds, fixed point classification using a phase portrait analysis, and solution behavior alsousing phase portrait analysis.The mathematical analysis should be accompanied by an explanation of its meaning in term of the quantities of interest.

Topic 6
Analyze the system to determine if there is a limit cycle under certain model parameter choices. This is an advanced topic that will require increased critical thinking and the learner is encouraged to use the discussion forum in the LMS to communicate with the rest of the classroom as well as the instructor.

Topic 7
Analyze the parameter space of the model and discuss its bifurcation patterns. The analysis should include bifurcation points, their classification, and any appropriate diagrams. This is also a rich topic, and it is encouraged that you consult with the instructor and other classmates before embarking in an analysis that exceeds the scope of this assignment.

Topic 8
Prepare an executive summary reportof the project. This report should contain:
• A two dimensional model with a clear description of its variables, parameter and terms
• Stability and Bifurcation analysis
• Conclusions

Reference no: EM133772074

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