On the relative position of limit cycles for the equation of type \((II)_{\ell =0}\) (Q795207)
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scientific article; zbMATH DE number 3861584
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the relative position of limit cycles for the equation of type \((II)_{\ell =0}\) |
scientific article; zbMATH DE number 3861584 |
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On the relative position of limit cycles for the equation of type \((II)_{\ell =0}\) (English)
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1984
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Consider the system \(x'=\delta x-y+mxy-y^ 2, y'=x+ax^ 2, a<0\), \(0<\delta \leq m\), \(m\leq(1/a)-a.\) Let \(\delta_ 0=(m/2)+(m^ 2/4a).\) It is proved that for \(\delta =\delta_ 0\) there is no limit cycle, for \(\delta_ 0<\delta \leq m\) there is no limit cycle around the focus at the origin and for \(0<\delta<\delta_ 0\) there is no limit cycle around the second focus.
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limit cycle
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focus
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