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Question: similar to firstorder equations we are often interested in bifurcations...

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Similar to first-order equations, we are often interested in bifurcations for first-order systems. For the following problems, find all bifurcation value(s) of a. You are looking for values of a where, for example, the equilibrium changes from being a spiral source to a saddle, source to sink, etc. First, begin by finding the eigenvalues in terms of a. Next, the two main techniques to find ion values are to determine where the discriminant (portion under the radical) is zero or where the eigenvalues are zero. Finally, consider the intervals between the bifurcation values and use a test point in each interval to determine the behavior of the equilibrium over that interval (much like checking increasing and decreasing for a function using its critical values in Calculus I). For each question, list all bifurcation values and list the behavior of the equilibrium in each interval (the intervals created by the bifurcation values). Y(t) 1. Y(t) 0 -5) Y(t) Y(t) 3. Y(t)
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