Dynamical behavior of almost periodically forced neutral delayed equation and its applications

Zhou, Hui

doi:10.1090/proc/16053

Dynamical behavior of almost periodically forced neutral delayed equation and its applications
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Proc. Amer. Math. Soc. 150 (2022), 5293-5309 Request permission

Abstract:

In this paper, we consider a class of almost periodically forced neutral delayed equation, which arises from population model with delays. A threshold parameter in terms of basic reproduction ratio $R_0$ is introduced into this neutral system. We derive the strongly subhomonogenous property of skew-product semiflow generated by the linearized neutral system under the assumptions of non-neutral case. We show that the positive almost periodic solution is globally stable by applying the approach of monotone skew-product semiflow. Finally, as a classical example, we illustrate the asymptotic behavior of Nicholson model with neutral type delays by using of the new theoretical results. The dynamical behaviors of neutral delayed equation forced by almost periods in this paper cover automatically some known ones of the non-neutral cases.

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