Periodic orbits and the global attractor for delayed monotone negative feedback

T. Krisztin, Bolyai Institute, Szeged, Hungary

E. J. Qualitative Theory of Diff. Equ., Proc. 6'th Coll. Qualitative Theory of Diff. Equ., No. 15. (2000), pp. 1-12.

Abstract: We study the delay differential equation $\dot x(t)=-\mu x(t)+f(x(t-1))$ with $\mu\ge 0$ and $C^1$-smooth real functions $f$ satisfying $f(0)=0$ and $f'<0$. For a set of $\mu$ and $f$, we determine the number of periodic orbits, and describe the structure of the global attractor as the union of the strong unstable sets of the periodic orbits and of the stationary point $0$.

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