Each of Problems 1 through 5 can be interpreted as describing the interaction of two species with population densities
a) Draw a direction field and describe how solutions seem to behave.
b) Find the critical points.
c) For each critical point, find the corresponding linearsystem. Find the eigenvalues and eigenvectors of the linear system. Classify each critical point as to type, anddetermine whether it is asymptotically stable, stable, orunstable.
d) Sketch the trajectories in the neighborhood of each critical point.
e) Draw a phase portrait for the system.
f) Determine the limiting behavior of
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Differential Equations: An Introduction to Modern Methods and Applications
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