A sufficient and necessary condition for the existence of a double bun type separatrix cycle for axial symmetry cubic systems (Q2780918)
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scientific article; zbMATH DE number 1720121
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A sufficient and necessary condition for the existence of a double bun type separatrix cycle for axial symmetry cubic systems |
scientific article; zbMATH DE number 1720121 |
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12 January 2003
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cubic system
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algebraic invariant curve
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phase portrait
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A sufficient and necessary condition for the existence of a double bun type separatrix cycle for axial symmetry cubic systems (English)
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The authors characterize all planar cubic systems that have the invariant algebraic curve \(x^4-x^2y+y^3=0.\) They study the cases in which the two loops that this curve possesses are homoclinic loops. The explicit characterization of these cases is done under the additional assumption that the cubic system is symmetric with respect to the \(y-\)axis. To end the paper, the phase portrait in the Poincaré sphere for these systems is given.
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0.8163302540779114
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