Hopf bifurcation and multiple periodic solutions in a damped harmonic oscillator with delayed feedback

• Autores: Jianzhi Cao, Rong Yuan, Haijun Jiang, Juan Song
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 263, Nº 1, 2014, págs. 14-24
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.11.015
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• Resumen

  • The purpose of this manuscript is to study the dynamics of a damped harmonic oscillator with delayed feedback. Different to previous papers, the bifurcation when the linearization at an equilibrium has, for critical value of the parameters, a pair of non-semisimple purely imaginary eigenvalues with geometric multiplicity one and algebraic multiplicity two is considered. By employing the Lyapunov�Schmidt reduction, the criteria for the existence and number of branches of bifurcating periodic solutions are derived. Finally, some numerical simulations are given to support the analytic results.