The corresponding eigenvector is one of the complex

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Unformatted text preview: ce the equilibrium solutio represents a stable node, which attracts all solutions. . If the condition in Part is not satisfied, that is, , then the real part of the eigenvalues is As long as the parameters are all positive, then the solutions will still converge to the equilibrium point . ________________________________________________________________________ page 381 —————————————————————————— CHAPTER 7. —— Section 7.6 2. Setting x results in the algebraic equations . For a nonzero solution, we require that A I . The roots of the characteristic equation are . Substituting , the two and equations reduce to . The two eigenvectors are Hence one of the complex-valued solutions is given by x Based on the real and imaginary parts of this solution, the general solution is x 3. Solution of the ODEs is based on the analysis of the algebraic equations . For a nonzero solution, we require that A I . The roots of the characteristic equation are . Setting , the equations are equivalent to . The eigenvectors...
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This note was uploaded on 03/11/2014 for the course MA 303 taught by Professor Staff during the Spring '08 term at Purdue.

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