A numerical study of spontaneous bifurcation
The author considers the following problem \((1)\quad u''+f(u)=0,| x| <L\), \(u(\pm L)=0\), where \(f(u)=-u(u-a)(u-b)\), with \(0<a<b\). This problem, which has been of recent interest, is studied numerically. It is shown that a two-sheeted surface of bifurcating solutions in the parameter space \(\{(a,L,u_ 1):\) \(0<a<b\), \(L>0\), \(u_ 1\in {\mathbb{R}}\}\), can be determined numerically, thus giving a complete numerical description of the solution set of (1) and its bifurcations. Discussion on continuation algorithms and numerical results conclude the paper.
two-sheeted surface of bifurcating solutions
scientific article; zbMATH DE number 4045049