Analysis of global bifurcation for a class of systems of degree five (Q1270880)
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scientific article; zbMATH DE number 1218604
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Analysis of global bifurcation for a class of systems of degree five |
scientific article; zbMATH DE number 1218604 |
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Analysis of global bifurcation for a class of systems of degree five (English)
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3 November 1998
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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.
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global bifurcation
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limit cycle
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separatrix loop bifurcation
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