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- W2952893235 abstract "In the paper [Large-amplitude periodic solutions for differential equations with delayed monotone positive feedback, JDDE 23 (2011), no. 4, 727--790], we have constructed large-amplitude periodic orbits for an equation with delayed monotone positive feedback. We have shown that the unstable sets of the large-amplitude periodic orbits constitute the global attractor besides spindle-like structures. In this paper we focus on a large-amplitude periodic orbit $mathcal{O}_{p}$ with two Floquet multipliers outside the unit circle, and we intend to characterize the geometric structure of its unstable set $mathcal{W}^{u}left(mathcal{O}_{p}right)$. We prove that $mathcal{W}^{u}left(mathcal{O}_{p}right)$ is a three-dimensional $C^{1}$-submanifold of the phase space and admits a smooth global graph representation. Within $mathcal{W}^{u}left(mathcal{O}_{p}right)$, there exist heteroclinic connections from $mathcal{O}_{p}$ to three different periodic orbits. These connecting sets are two-dimensional $C^{1}$-submanifolds of $mathcal{W}^{u}left(mathcal{O}_{p}right)$ and homeomorphic to the two-dimensional open annulus. They form $C^{1}$-smooth separatrices in the sense that they divide the points of $mathcal{W}^{u}left(mathcal{O}_{p}right)$ into three subsets according to their $omega$-limit sets." @default.
- W2952893235 created "2019-06-27" @default.
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- W2952893235 date "2014-03-03" @default.
- W2952893235 modified "2023-09-27" @default.
- W2952893235 title "The unstable set of a periodic orbit for delayed positive feedback" @default.
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