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Localization of periodic orbits of polynomial vector fields of even degree by linear functions

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  • Starkov, Konstantin E.

Abstract

This paper is concerned with the localization problem of periodic orbits of polynomial vector fields of even degree by using linear functions. Conditions of the localization of all periodic orbits in sets of a simple structure are obtained. Our results are based on the solution of the conditional extremum problem and the application of homogeneous polynomial forms of even degrees. As examples, the Lanford system, the jerky system with one quadratic monomial and a quartically perturbed harmonic oscillator are considered.

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  • Starkov, Konstantin E., 2005. "Localization of periodic orbits of polynomial vector fields of even degree by linear functions," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 621-627.
    • Handle: RePEc:eee:chsofr:v:25:y:2005:i:3:p:621-627
    DOI: 10.1016/j.chaos.2004.11.052
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    References listed on IDEAS

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    1. Starkov, Konstantin E. & Krishchenko, Alexander P., 2005. "Localization of periodic orbits of polynomial systems by ellipsoidal estimates," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 981-988.
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    Cited by:

    1. Zhou, Xiaobing & Wu, Yue & Li, Yi & Wei, Zhengxi, 2008. "Hopf bifurcation analysis of the Liu system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1385-1391.
    2. Barrio, Roberto & Blesa, Fernando, 2009. "Systematic search of symmetric periodic orbits in 2DOF Hamiltonian systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 560-582.
    3. Ramos, J.I., 2006. "Determination of periodic orbits of nonlinear oscillators by means of piecewise-linearization methods," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1306-1313.

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