Detecting a Prey in a Spider Orb-Web from In-Plane Vibration
Abstract
Spiders perform a task similar to solving an inverse problem when detecting the position of a prey, a mate, or a predator perturbing the orb-web. Recent work has advanced in the study of the orb-web as a sensor when it is subjected to small transverse vibrations, using a continuous membrane model for the orb-web. However, in-plane vibrations have not been investigated yet as data for the prey detection problem. In the present work, we develop the structure of the small in-plane vibratory response of an axially symmetric orb-web supported at the boundary. Additionally, we prove that knowledge of the in-plane dynamic response inside an annulus centered at the origin of the orb-web, where the spider is assumed to stay for a sufficiently large registration time, allows us to determine uniquely the in-plane distributed load simulating the prey's impact. The theoretical outcome is illustrated with a numerical implementation of the reconstruction method.
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Information & Authors
Information
Published In
SIAM Journal on Applied Mathematics
Pages: 2297 - 2322
DOI: 10.1137/20M1372792
ISSN (online): 1095-712X
Copyright
© 2021, Society for Industrial and Applied Mathematics.
History
Submitted: 12 October 2020
Accepted: 15 July 2021
Published online: 1 November 2021
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Funding Information
Ministerio de Ciencia, Innovación y Universidades : PGC2018-098218-B-100
Fundação de Amparo à Pesquisa do Estado de São Paulo https://doi.org/10.13039/501100001807 : 2019/14827-0, 2019/24915-4
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Cited By
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- Determination of the prey impact region in a spider orb-web from in-plane vibrationApplied Mathematics and Computation, Vol. 424 | 1 Jul 2022
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