• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.643-653
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• 1998

In this paper, we analyze a system for an epidemiological model which has a double zero eigenvalue at certain parameter values.

• Communications of the Korean Mathematical Society
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• v.14 no.2
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• pp.441-447
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• 1999

A free boundary problem is derived from a singular limit system of a reaction diffusion equation whose reaction terms are bistable type. In this paper, we shall consider a free boundary problem with two layers satisfying the zero flux boundary condition and shall show that the Hopf bifurcation can not occur as a parameter varies.

• The Pure and Applied Mathematics
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• v.4 no.1
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• pp.61-69
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• 1997

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.