Analysis of global bifurcation for a class of systems of degree five. (English) Zbl 0994.34027
Consider the two-dimensional system
\[
dx/dt= y,\quad dy/dt= -x-(x^2- a)(1+ y^2)y,\tag{\(*\)}
\]
where \(a\) is a parameter. The authors give a complete bifurcation analysis of \((*)\) and prove that \((*)\) has a unique stable limit cycle for some parameter interval which is generated by a Hopf and a separatrix loop bifurcation correspondingly.
Reviewer: Klaus R.Schneider (Berlin)
MSC:
| 34C23 | Bifurcation theory for ordinary differential equations |
| 34C25 | Periodic solutions to ordinary differential equations |
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