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Bifurcation from a saddle connection in functional differential equations: An approach with inclination lemmas

Hans-Otto Walther — 1990

CONTENTSIntroduction...........................................................................................................................................5  I.........................................................................................................................................................151. Preliminaries...................................................................................................................................152. Solutions of a family of differential...

Smoothness of the attractor of almost all solutions of a delay differential equation

Walther Hans-Otto;  Yebdri Mustapha — 1997

AbstractLet a C¹-function f:ℝ → ℝ be given which satisfies f(0) = 0, f'(ξ) < 0 for all ξ ∈ ℝ, and sup f < ∞ or -∞ < inf f. Let C = C([-1,0],ℝ). For an open-dense set of initial data the phase curves [0,∞) → C given by the solutions [-1,∞) → ℝ to the negative feedback equationx'(t) = -μx(t) + f(x(t-1)), with μ > 0,are absorbed into the positively invariant set S ⊂ C of data ϕ ≠ 0 with at most one sign change. The global attractor A of the semiflow restricted to S̅ is either the singleton...

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