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almost periodic nicholson systems

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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The exponential ordering for nonautonomous delay systems with applications to compartmental Nicholson systems
Part of
- Smooth dynamical systems: general theory
Sylvia Novo, Rafael Obaya, Ana M. Sanz, Víctor M. Villarragut
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 154 / Issue 2 / April 2024

Published online by Cambridge University Press:

27 March 2023, pp. 568-599

Print publication:

April 2024
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The exponential ordering is exploited in the context of nonautonomous delay systems, inducing monotone skew-product semiflows under less restrictive conditions than usual. Some dynamical concepts linked to the order, such as semiequilibria, are considered for the exponential ordering, with implications for the determination of the presence of uniform persistence or the existence of global attractors. Also, some important conclusions on the long-term dynamics and attraction are obtained for monotone and sublinear delay systems for this ordering. The results are then applied to almost periodic Nicholson systems and new conditions are given for the existence of a unique almost periodic positive solution which asymptotically attracts every other positive solution.