The Two-Dimensional Attractor of a Differential ... - Springer Link

with +>0 and smooth real functions f, r satisfying f(0)=0, f $
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Journal of Dynamics and Differential Equations, Vol. 13, No. 3, 2001

The Two-Dimensional Attractor of a Differential Equation with State-Dependent Delay Tibor Krisztin 1, 3 and Ovide Arino 2 Received August 25, 1999 The delay differential equation x* (t)=&+x(t)+ f (x(t&r)),

r=r(x(t))

with +>0 and smooth real functions f, r satisfying f (0)=0, f $0 for all + u # I+ r . Choose c, d # (0, ] such that I r =(&d, c). Clearly, &&b&d