Hopf-Pitchfork bifurcation in a simplified BAM neural network model with multiple delays

• Autores: Tao Dong, Xiaofeng Liao
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 253, Nº 1, 2013, págs. 222-234
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.04.027
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• Resumen

  • In this paper, a simplified BAM neural network model with multiple delays is considered.

    By studying the distribution of the eigenvalues of the associated characteristic equation, we derive the critical values where Hopf�Pitchfork bifurcation occurs. Then, by computing the normal forms for the system, the bifurcation diagrams are obtained. Furthermore, we carry out bifurcation analysis and numerical simulations showing that there exist a stable fixed point, a pair of stable fixed points, a stable periodic solution, and co-existence of a pair of stable periodic solution in the neighborhood of the Hopf�Pitchfork critical point.