title: ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ¸ÑÑÐµÐ¼Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ Ð´Ð¸ÑÑÑÐ·Ð¸Ð¸ Ñ ÑÐµÐ°ÐºÑÐ¸ÐµÐ¹, ÑÐ²ÑÐ·Ð°Ð½Ð½Ð¾Ð¹ Ñ ÑÐ¾ÑÐ¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸ÐµÐ¼ ÑÐµÑÑÐ°ÑÐºÐ¸ Ð³Ð»Ð°Ð·Ð° ÐÑÐ¾Ð·Ð¾ÑÐ¸Ð»Ñ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Investigation of a reaction-diffusion system, related to patterning of the Drosophila eye
Creators: name: ÐÐ°ÑÑ, Ð¡Ð²ÐµÑÐ»Ð°Ð½Ð°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2020
Subjects: Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²ÐµÐ½Ð½Ð¾-Ð½ÐµÐ¿ÑÐµÑÑÐ²Ð½Ð°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ Ð´Ð¸ÑÑÑÐ·Ð¸Ð¸ Ñ ÑÐµÐ°ÐºÑÐ¸ÐµÐ¹
Ð´Ð¸ÑÑÑÐ·Ð¸Ð¾Ð½Ð½Ð°Ñ Ð½ÐµÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÑ
Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð½ÐµÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ Ð¿Ð¾ Ð¢ÑÑÑÐ¸Ð½Ð³Ñ
spatially-continuous reaction-diffusion model
diffusion-driven instability
studying of Turing instability

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description: This paper is devoted to investigation of a reaction-diffusion system, related to patterning of R8-photoreceptors in the Drosophila eye retina. The research set the following goals: 1. Rewrite the governing reaction-diffusion system in dimensionless form. 2. Determine isoclines of a reaction-diffusion system and system of equations defining homogeneous steady-states in some particular cases. 3. Determine if reaction-diffusion system exhibits any diffusion-driven instability without morphogenetic furrow. 4. Determine whether is trivial homogeneous steady-state unstable in terms of Turing instability. 5. Define parameter space of Turing instability for trivial homogeneous steady-state in case of first degree Hills' functions. Different approaches based on classical continuous analysis to determine whether is any Turing instability of reaction-diffusion system were described in this paper. The study resulted into asymptotically defined parameter space of Turing instability for trivial homogeneous steady-state. The results of the investigation also proved that given reaction-diffusion system describes the process of R8-photoreceptors patterning correctly.