Periodic solutions for differential equations with state-dependent delay and positive feedback

Existence of a nontrivial periodic orbit and a homoclinic orbit connecting 0 to the periodic orbit is shown for the differential equation x'(t)=-µx(t) + f(x(t-r)), r = r(x(t)) with state-dependent delay and positive feedback. Here µ > 0, f and r are smooth real functions with r(0)=1 and f' > 0.

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