Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T11:14:53.040328Z
Paper Citation Record · LEDGER
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics
As of 16 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 1 inbound Pith citation observation for arXiv:1908.09495.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-14T12:30:05.564669Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-14T12:30:05.777481Z
Reference resolution
36 of 36 outbound references displayed
- verified exact0
- verified fuzzy32
- unresolved4
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 4b5ca4be-56cc-4d7b-9cf0-2c9c679513a2 · outbound
This paper cites Diffusion driven instability in an inhomogeneous domain.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Diffusion driven instability in an inhomogeneous domain
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.615999Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d53dafbd-8aa9-4f7d-878f-faae6753bfc7 · outbound
This paper cites Spatio-temporal pattern for- mation on spherical surfaces: numerical simulation and application to solid tumour growth.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Spatio-temporal pattern for- mation on spherical surfaces: numerical simulation and application to solid tumour growth
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.601188Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c6f8d27e-100e-40ff-b3e9-7db0918e559a · outbound
This paper cites Thick and thin fingers point out turing waves.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Thick and thin fingers point out turing waves
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.586413Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2171e016-6abe-4ee4-8a12-923a767bda24 · outbound
This paper cites Periodic stripe formation by a turing mechanism operationg at growth zones in the mammalian palate.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Periodic stripe formation by a turing mechanism operationg at growth zones in the mammalian palate
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.570998Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a14e4c69-7489-401d-83b7-9a0b086a478c · outbound
This paper cites A theory of biological pattern formation.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics A theory of biological pattern formation
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.556397Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c74fda81-2e86-4469-b7ee-361ead6cebb1 · outbound
This paper cites Interaction of turing patterns with an external linear morphogen gradient.Nonlinearity, 22(10):2541, 2009.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Interaction of turing patterns with an external linear morphogen gradient.Nonlinearity, 22(10):2541, 2009
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.542069Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c3e375ff-3fc8-4cde-9626-7585263dcf02 · outbound
This paper cites Stability of turing-type patterns in a reaction–diffusion system with an external gradient.International Journal of Bifurcation and Chaos, 27(01):1750003, 2017.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Stability of turing-type patterns in a reaction–diffusion system with an external gradient.International Journal of Bifurcation and Chaos, 27(01):1750003, 2017
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.527753Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e7302362-201c-4bfb-ab6f-bb9301f1ae00 · outbound
This paper cites an unresolved cited work.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:14:53.513093Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 5766b86b-a963-48df-91f1-166d371b7922 · outbound
This paper cites an unresolved cited work.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:14:53.498454Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 13cd5e11-00f6-47c3-b042-3169d8ddaf04 · outbound
This paper cites Positional information and reaction-diffusion: two big ideas in developmental biology combine.Development, 142:1203–1211, 2015.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Positional information and reaction-diffusion: two big ideas in developmental biology combine.Development, 142:1203–1211, 2015
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.482417Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 28d5efbd-2aee-4889-b2b8-72b03a04862f · outbound
This paper cites Iron and M.
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.468026Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2e6c7d9b-3d4b-4ec1-aa55-3b3d9cf15fc4 · outbound
This paper cites Significance of non-normality-induced patterns: Transient growth versus asymp- totic stability.Chaos: An Interdisciplinary Journal of Nonlinear Science, 27(7):073120, 2017.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Significance of non-normality-induced patterns: Transient growth versus asymp- totic stability.Chaos: An Interdisciplinary Journal of Nonlinear Science, 27(7):073120, 2017
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.452690Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation dea22071-0b18-4754-be20-f01e3d47dd5d · outbound
This paper cites Theinfluenceofreceptor- mediated interactions on reaction-diffusion mechanisms of cellular self-organisation.Bulletin of Mathematical Biology, 74(4):935–957, Apr 2012.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Theinfluenceofreceptor- mediated interactions on reaction-diffusion mechanisms of cellular self-organisation.Bulletin of Mathematical Biology, 74(4):935–957, Apr 2012
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.437594Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 503d6699-dd24-420d-9037-690c2ef310d8 · outbound
This paper cites Domain size driven instability: Self- organization in systems with advection.SIAM Journal on Applied Mathematics, 78(5):2298– 2322, 2018.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Domain size driven instability: Self- organization in systems with advection.SIAM Journal on Applied Mathematics, 78(5):2298– 2322, 2018
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.422587Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 057b41cb-ea61-477b-9507-6b1c8045c02d · outbound
This paper cites Reaction-diffusion model as a framework for understanding biological pattern formation.Science, 329(5999):1616–1620, 2010.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Reaction-diffusion model as a framework for understanding biological pattern formation.Science, 329(5999):1616–1620, 2010
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.408352Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation eec5380c-b11c-4542-bfb3-9c38457f14e0 · outbound
This paper cites Krause, Václav Klika, Thomas E.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Krause, Václav Klika, Thomas E
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.393027Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 844d2cc4-3843-4964-939c-bea4ee2738fe · outbound
This paper cites Theturingmodelcomesofmolecular age.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Theturingmodelcomesofmolecular age
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.378276Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f785d639-f6bc-479e-80e5-dcb98cfcae66 · outbound
This paper cites Spatial periodic forcing can displace patterns it is intended to control.Physical review letters, 109(3):034102, 2012.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Spatial periodic forcing can displace patterns it is intended to control.Physical review letters, 109(3):034102, 2012
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.363115Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 865d57ed-4ce2-4adf-9dad-3c8de4abfeae · outbound
This paper cites Effect of axial growth on turing pattern formation.Physical review letters, 96(4):048304, 2006.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Effect of axial growth on turing pattern formation.Physical review letters, 96(4):048304, 2006
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.347898Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 43af5a39-f9e2-4745-a6a8-274093b2f515 · outbound
This paper cites Turing and wopert work together during limb development.Science Signaling, 6(270):1–3, 2013.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Turing and wopert work together during limb development.Science Signaling, 6(270):1–3, 2013
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.333186Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 15c4c061-5944-463e-b293-0aaf76180f6a · outbound
This paper cites Mathematical Biology.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Mathematical Biology
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.317916Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3b49fc64-0981-433d-9c26-3035f7e29c89 · outbound
This paper cites Interactions between ze- brafish pigment cells responsible for the generation of turing patterns.PNAS, 106(21):8429– 8434, 2009.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Interactions between ze- brafish pigment cells responsible for the generation of turing patterns.PNAS, 106(21):8429– 8434, 2009
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.302305Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b3c170b2-a2d7-4e7a-87ac-5b6b9b2f8efb · outbound
This paper cites Pattern formation in spatially hetero- geneous turing reaction–diffusion models.Physica D: Nonlinear Phenomena, 181(1):80–101, 2003.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Pattern formation in spatially hetero- geneous turing reaction–diffusion models.Physica D: Nonlinear Phenomena, 181(1):80–101, 2003
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.286794Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a8dd5e92-05b6-4883-a0e1-d7911a8b84d6 · outbound
This paper cites Complex pattern formation in reaction–diffusion systems with spatially varying parameters.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Complex pattern formation in reaction–diffusion systems with spatially varying parameters
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.270550Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e55d41ba-f86e-49d6-8cda-bb606bb79aa1 · outbound
This paper cites Towards an integrated experimental–theoretical approach for assessing the mechanistic basis of hair and feather mor- phogenesis.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Towards an integrated experimental–theoretical approach for assessing the mechanistic basis of hair and feather mor- phogenesis
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.254779Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4e6f0281-45ba-4b93-86ca-f747a7ec78eb · outbound
This paper cites Patterning of palatal rugae through sequential addition reveals an anterior/posterior boundary in palatal development.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Patterning of palatal rugae through sequential addition reveals an anterior/posterior boundary in palatal development
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.239266Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3dda9a89-5524-4f6b-b124-6bd2b7a06189 · outbound
This paper cites an unresolved cited work.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Unresolved cited work
Reference 27
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:14:53.223920Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 552fc04d-3fb1-47f1-b9c3-e1563346380c · outbound
This paper cites Digit patterning is controlled by a bmp-sox9- wnt turing network modulated by morphogen gradients.Science, 345(6196):266–570, 2014.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Digit patterning is controlled by a bmp-sox9- wnt turing network modulated by morphogen gradients.Science, 345(6196):266–570, 2014
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.209491Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation cf9a6423-e7eb-4959-883b-adee1ae482cf · outbound
This paper cites Simple chemical reaction systems with limit cycle behaviour.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Simple chemical reaction systems with limit cycle behaviour
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.194013Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3afb907c-babb-4e6a-9110-66a8b4f77937 · outbound
This paper cites Hox genes regulate digit patterning by controlling the wavelength of a turing-type mechanism.Science, 338(1476):1476–1480, 2012.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Hox genes regulate digit patterning by controlling the wavelength of a turing-type mechanism.Science, 338(1476):1476–1480, 2012
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.177720Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 921febe6-6981-4e14-ae02-8a5d9aa061ce · outbound
This paper cites an unresolved cited work.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Unresolved cited work
Reference 31
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:14:53.160685Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 31f0bb60-fa9e-4cbf-b0ff-d39be45415df · outbound
This paper cites The chemical basis of morphogenesis.Philosophical Transactions of the Royal Society of London B: Biological Sciences, 237(641):37–72, 1952.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics The chemical basis of morphogenesis.Philosophical Transactions of the Royal Society of London B: Biological Sciences, 237(641):37–72, 1952
Reference 32
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.142158Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d8367ae8-8652-4eea-af77-e3898297bc6b · outbound
This paper cites The dynamics and pinning of a spike for a reaction-diffusion system.SIAM Journal on Applied Mathematics, 62(4):1297–1328, 2002.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics The dynamics and pinning of a spike for a reaction-diffusion system.SIAM Journal on Applied Mathematics, 62(4):1297–1328, 2002
Reference 33
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.126083Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8709a8f1-6af8-40c2-ae48-d09d652af253 · outbound
This paper cites Warmflash, B.
Reference 34
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.110039Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ebe930e6-0e92-4360-88d6-d054aed8c794 · outbound
This paper cites Spikes for the gierer–meinhardt system with discontinuous diffusion coefficients.Journal of Nonlinear Science, 19(3):301–339, 2009.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Spikes for the gierer–meinhardt system with discontinuous diffusion coefficients.Journal of Nonlinear Science, 19(3):301–339, 2009
Reference 35
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.094645Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 5f61301f-8631-4f64-bbbd-1ba1bdf4ece6 · outbound
This paper cites Positional infromation and the spatial pattern of cellular differentiation.J.
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics Positional infromation and the spatial pattern of cellular differentiation.J
Reference 36
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:14:53.079089Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Pith citing papers
Observation 0b45389b-f996-45b0-9b51-0b1894b8491f · inbound
From One Pattern into Another: Analysis of Turing Patterns in Heterogeneous Domains via WKBJ cites this paper.
From One Pattern into Another: Analysis of Turing Patterns in Heterogeneous Domains via WKBJ Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics
Reference 36
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T12:30:05.785030Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.