The interaction of two populations of animals is modeled by the differential equations
Chapter 9, Problem 47(choose chapter or problem)
The interaction of two populations of animals is modeled by the differential equations dx - x -t- ky dtdy_ dt= kx Ayfor some positive constant k. a. What kind of interaction do we observe? What is the practical significance of the constant k? b. Find the eigenvalues of the coefficient matrix of the system. What can you say about the signs of these eigenvalues? How does your answer depend on the value of the constant k ? c. For each case you discussed in part (b), sketch a rough phase portrait. What does each phase portrait tell you about the future of the two populations?
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