Computation of Invariant Curves and Identifying the Type of Critical Point
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This paper considers two dimensional systems which have purely imaginary eigenvalues. In order to obtain more propositions of invariant curves, the authors transform the real systems into complex differential systems by using a suitable linear transformation. The authors also propose an algorithm to compute exponential factors. An improved method of constructing integrating factor by using all invariant curves is presented and can be used in determining the type of the equilibrium points.
KeywordsComplex differential system equilibrium point exponential factor invariant curve
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- Darboux G. Mémoire sur leséquations différentielles algébriques du premier ordre et du premier degré (Mélanges), Bull. Sci. Math., 1878, 2: 151–200.Google Scholar