Preservation of Hopf bifurcation for neutral delay-differential equations by 0-methods

• Autores: Huan Su, Wenxue Li, Xiaohua Ding
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 248, Nº 1, 2013, págs. 76-87
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.01.020
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• Resumen

  • This paper considers the preservation of Hopf bifurcation of some neural delay-differential equations by è-method. By analyzing the dynamics of the numerical discrete system derived by è-method, we show that è-method could inherit the Hopf bifurcation and the asymptotical stability for sufficiently small stepsize h = 1/m, wheremis a positive integer.

    In particular, for è = 1/2 the result holds for any stepsize h = 1/m. Furthermore, the stability of the closed invariant curve is established. Finally, some numerical examples are illustrated to support the analytic results.