On the number of limit cycles of a \(Z_{4}\)-equivariant quintic polynomial system (Q984330)
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scientific article; zbMATH DE number 5757564
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the number of limit cycles of a \(Z_{4}\)-equivariant quintic polynomial system |
scientific article; zbMATH DE number 5757564 |
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On the number of limit cycles of a \(Z_{4}\)-equivariant quintic polynomial system (English)
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19 July 2010
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The authors study limit cycles of the near-Hamiltonian \(\mathbb{Z}_4\)-equivariant polynomial system \[ \dot x=H_y+\epsilon P_5(x,y), \quad \dot y=-H_x+\epsilon Q_5(x,y) \tag{1} \] with the Hamiltonian \(H=-2 (x^2+y^2)+(x^4+y^4)\) and \(P_5, Q_5\) being some polynomials of degree five. Using the methods of Hopf and heteroclinic bifurcation, it is shown that system (1) can have 13 limit cycles.
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limit cycle
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polynomial system
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heteroclinic loop
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\(\mathbb{Z}_4\)-equivariance
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Hopf bifurcation
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