Searching for Complexity in the Human Pupillary Light Reflex

Rosário D. Laureano, Diana Mendes, Clara Grácio and Fátima Laureano
Additional contact information
Rosário D. Laureano: Department of Mathematics, ISTAR-IUL Information Sciences, Technologies and Architecture Research Center, ISCTE-IUL Lisbon University Institute, Avenida das Forças Armadas, 1649-026 Lisboa, Portugal
Diana Mendes: Department of Quantitative Methods for Management and Economics, BRU-IUL Business Research Unit, ISCTE-IUL Lisbon University Institute, Avenida das Forças Armadas, 1649-026 Lisboa, Portugal
Clara Grácio: Department of Mathematics, CIMA-Research Centre for Mathematics and Applications, Universidade de Évora, Rua Romão Ramalho, 59,7000-585 Évora, Portugal
Fátima Laureano: Instituto de Microcirurgia Ocular, Torres de Lisboa, Rua Tomás da Fonseca, 1600-209 Lisboa, Portugal

Mathematics, 2020, vol. 8, issue 3, 1-14

Abstract: This article aims to examine the dynamical characteristics of the pupillary light reflex and to provide a contribution towards their explanation based on the nonlinear theory of dynamical systems. To introduce the necessary concepts, terminology, and relevant features of the pupillary light reflex and its associated delay, we start with an overview of the human eye anatomy and physiology with emphasis on the iris, pupil, and retina. We also present the most highly regarded models for pupil dynamics found in the current scientific literature. Then we consider the model developed by Longtin and Milton, which models the human pupillary light reflex, defined by a nonlinear differential equation with delay, and present our study carried out on the qualitative and quantitative dynamic behavior of that neurophysiological control system.

Keywords: pupil; delay differential equations; dynamic stability; Andronov–Hopf bifurcation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/3/394/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/3/394/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:3:p:394-:d:330957

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().