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Differential Equations : Bifurcations in Linear Systems

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In Chapter 3, we have studied techniques for solving linear systems. Given the coefficient matrix for the system, we can use these techniques to classify the system, describe the qualitative behavior of solutions, and give a formula for the general solution. In this lab we consider a two-parameter family of linear systems. The goal is to better understand how different linear systems are related to each other, or in other words, what bifurcations occur in parameterized families of linear systems.
Consider the linear system
dx/dt =ax+by
where a and b are parameters that can take on any real value. In your report, address the following items:

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Bifurcations in Linear Systems of Differential Equations are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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