AN UNFOLDING OF DEGENERATE EQUILIBRIA WITH LINEAR PART $\chi$'v= y, y' = 0

  • Published : 1997.06.01

Abstract

In this paper, we study the dynamics of a two-parameter unfolding system $\chi$' = y, y' = $\beta$y+$\alpha$f($\chi\alpha\pm\chiy$+yg($\chi$), where f($\chi$,$\alpha$) is a second order polynomial in $\chi$ and g($\chi$) is strictly nonlinear in $\chi$. We show that the higher order term yg($\chi$) in the system does not change qulitative structure of the Hopf bifurcations near the fixed points for small $\alpha$ and $\beta$ if the nontrivial fixed point approaches to the origin as $\alpha$ approaches zero.

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