File:4-limit-cycles-quadratic-system-16-Hilbert-problem.jpg
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Four limit cycles in two-dimensional quadratic polynomial system (16th Hilbert problem)
Summary
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English: Four limit cycles in two-dimensional quadratic polynomial system (16th Hilbert problem): x' = −(a1x2 + b1xy + c1y2 + α1x + β1y), y' = −(a2x2 + b2xy + c2y2 + α2x + β2y) for the coefficients a1 = b1 = β1 = −1, c1 = α1 = 0, b2 = −2.2, c2 = −0.7, a2 = 10, α2 = 72.7778, and β2 = −0.0015. Limit cycles L1,L2,L3,L4 (green color represents stable and red represents unstable). One limit cycle L4 (self-excited periodic attractor) around an unstable equilibrium (red dot) is shown in (a), while the localization of three nested limit cycles
(L1,2,3; L2 is a hidden periodic attractor) around stable zero equilibrium (green dot) is presented in (b). N.V. Kuznetsov, O.A. Kuznetsova, G.A. Leonov, Visualization of four normal size limit cycles in two-dimensional polynomial quadratic system, Differential Equations and Dynamical Systems, 21(1-2), 2013, pp. 29-33 (https://dx.doi.org/10.1007/s12591-012-0118-6) |
| Date | |
| Source | Own work |
| Author | Kuznetsov N.V. |
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| current | 11:34, 22 March 2019 | | 3,006 × 1,178 (236 KB) | Kuznetsov N.V. (talk | contribs) | User created page with UploadWizard |
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