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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
page 381 —————————————————————————— CHAPTER 7. ——
2. Setting x results in the algebraic equations
. For a nonzero solution, we require that
. The roots of
the characteristic equation are
, the two
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
. The roots of the
characteristic equation are
, 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.
- Spring '08