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2 results

  • Hopf Bifurcation for Implicit Neutral Functional Differential Equations

  • Tomasz Kaczynski, Huaxing Xia
  • Journal:
    Canadian Mathematical Bulletin / Volume 36 / Issue 3 / 01 September 1993
    Published online by Cambridge University Press:
    20 November 2018, pp. 286-295
    Print publication:
    01 September 1993
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  • An analog of the Hopf bifurcation theorem is proved for implicit neutral functional differential equations of the form F(xt, D′(xt, α), α) = 0. The proof is based on the method of S1-degree of convex-valued mappings. Examples illustrating the theorem are provided.

  • A Local Hopf Bifurcation Theorem for a Certain Class of Implicit Differential Equations

  • Tomasz Kaczynski, Wieslaw Krawcewicz
  • Journal:
    Canadian Mathematical Bulletin / Volume 36 / Issue 2 / 01 June 1993
    Published online by Cambridge University Press:
    20 November 2018, pp. 183-189
    Print publication:
    01 June 1993
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  • The local Hopf Bifurcation theorem is extended to implicit differential equations in Rn, of the form ẋ = f(x,ẋ, α), which are not solvable for the variable ẋ. The proof uses the S1 -degree of convex-valued mappings. An example of an implicit differential equation in R3 to which the presented theorem applies is provided.