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Open AccessArticle

Searching for Complexity in the Human Pupillary Light Reflex

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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
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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
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Department of Mathematics, CIMA-Research Centre for Mathematics and Applications, Universidade de Évora, Rua Romão Ramalho, 59,7000-585 Évora, Portugal
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Instituto de Microcirurgia Ocular, Torres de Lisboa, Rua Tomás da Fonseca, 1600-209 Lisboa, Portugal
*
Author to whom correspondence should be addressed.
Current address: Department of Mathematics, CIMA-Research Centre for Mathematics and Applications, Universidade de Évora, Rua Romão Ramalho, 59,7000-585 Évora, Portugal.
Mathematics 2020, 8(3), 394; https://doi.org/10.3390/math8030394
Received: 14 January 2020 / Revised: 4 March 2020 / Accepted: 8 March 2020 / Published: 11 March 2020
(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations)
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. View Full-Text
Keywords: pupil; delay differential equations; dynamic stability; Andronov–Hopf bifurcation pupil; delay differential equations; dynamic stability; Andronov–Hopf bifurcation
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MDPI and ACS Style

Laureano, R.D.; Mendes, D.; Grácio, C.; Laureano, F. Searching for Complexity in the Human Pupillary Light Reflex. Mathematics 2020, 8, 394.

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