Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-06-26T07:43:48.390934Z
Paper Citation Record · LEDGER
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems
As of 12 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 1 inbound Pith citation observation for arXiv:2606.23211.
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 2026-08-12T06:34:41.77262+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-05T14:51:09.697264Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-05T14:51:09.859056Z
Reference resolution
30 of 30 outbound references displayed
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External citation measurements
No source-named external measurement is stored.
Outbound references
Observation f27761ff-cd37-407f-ad31-2debbb108a5c · outbound
This paper cites Adaptive POD-DEIM correction for Turing pattern approxi- mation in reaction–diffusion PDE systems.Journal of Numerical Mathematics, 31(3):205–229, 2023.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Adaptive POD-DEIM correction for Turing pattern approxi- mation in reaction–diffusion PDE systems.Journal of Numerical Mathematics, 31(3):205–229, 2023
Reference 1
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T07:43:48.390934Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 85cb58f1-7e20-488b-8c4b-5b4382992916 · outbound
This paper cites Piecewise DMD for oscillatory and Turing spatio-temporal dynamics.Computers & Mathematics with Applications, 160:108–124, 2024.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Piecewise DMD for oscillatory and Turing spatio-temporal dynamics.Computers & Mathematics with Applications, 160:108–124, 2024
Reference 2
- Resolution
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3576409b-9971-4a31-81b5-25fa2d83865d · outbound
This paper cites A structure-preserving ldg discretization of the fisher-kolmogorov equation for modeling neurodegenerative diseases.Mathematics and Computers in Simulation, 2025.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems A structure-preserving ldg discretization of the fisher-kolmogorov equation for modeling neurodegenerative diseases.Mathematics and Computers in Simulation, 2025
Reference 3
- Resolution
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation aff5a2ca-1564-473b-9ffc-a236caf5c663 · outbound
This paper cites Chapman and Hall/CRC, 2016.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Chapman and Hall/CRC, 2016
Reference 4
- Resolution
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 65e3bb88-41fe-4d3d-a2a8-10eadb57ba6a · outbound
This paper cites Positivity-preserving methods for ordinary differential equa- tions.ESAIM: Mathematical Modelling and Numerical Analysis, 56(6):1843–1870, 2022.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Positivity-preserving methods for ordinary differential equa- tions.ESAIM: Mathematical Modelling and Numerical Analysis, 56(6):1843–1870, 2022
Reference 5
- Resolution
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a843eb78-3845-4b95-b17c-f8d32dd585e1 · outbound
This paper cites Weakly nonlinear analysis of turing patterns in a morphochemical model for metal growth.Computers & Mathematics with Applications, 70(8):1948–1969, 2015.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Weakly nonlinear analysis of turing patterns in a morphochemical model for metal growth.Computers & Mathematics with Applications, 70(8):1948–1969, 2015
Reference 6
- Resolution
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 90f4735d-04b3-4dfe-bf64-ed85476b646e · outbound
This paper cites A semi- automatic numerical algorithm for turing patterns formation in a reaction-diffusion model.IEEE Access, 6:4720– 4724, 2017.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems A semi- automatic numerical algorithm for turing patterns formation in a reaction-diffusion model.IEEE Access, 6:4720– 4724, 2017
Reference 7
- Resolution
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 32b37518-f1df-454e-a4cb-736f4e50e5f2 · outbound
This paper cites General runge– kutta tase methods for reaction–diffusion problems: D.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems General runge– kutta tase methods for reaction–diffusion problems: D
Reference 8
- Resolution
- unresolved
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 81e1bc5f-66d8-4277-9356-2e06ce68121c · outbound
This paper cites Matrix-oriented discretization methods for reaction-diffusion PDEs: comparisons and applications.Computers & Mathematics with Applications, 78(8):2067–2085, 2019.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Matrix-oriented discretization methods for reaction-diffusion PDEs: comparisons and applications.Computers & Mathematics with Applications, 78(8):2067–2085, 2019
Reference 9
- Resolution
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 992f36a8-bdfd-4de9-93a3-312e32198f5a · outbound
This paper cites Numerical analysis of a first-order in time implicit- symplectic scheme for predator–prey systems.Computers & Mathematics with Applications, 74(5):948–961, 2017.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Numerical analysis of a first-order in time implicit- symplectic scheme for predator–prey systems.Computers & Mathematics with Applications, 74(5):948–961, 2017
Reference 10
- Resolution
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7a620296-7be2-4c2f-bbdd-1429fb7a1788 · outbound
This paper cites Krause, Deborah Lacitignola, Carmela Marangi, Angela Monti, and Edgardo Villar- Sepúlveda.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Krause, Deborah Lacitignola, Carmela Marangi, Angela Monti, and Edgardo Villar- Sepúlveda
Reference 11
- Resolution
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- no resolver link, observed 2026-06-26T07:43:48.390934Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7551c9f6-3728-4279-bf43-015bb548b88c · outbound
This paper cites Geometric numerical integration in ecological modelling.Mathematics, 8(1):25, 2020.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Geometric numerical integration in ecological modelling.Mathematics, 8(1):25, 2020
Reference 12
- Resolution
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- no resolver link, observed 2026-06-26T07:43:48.390934Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c8ca312e-ea7e-4511-bdd6-a4a9b9d6d5cc · outbound
This paper cites Adapted imex numerical methods for reaction-diffusion problems.International journal of circuits, systems and signal processing, 13:507–515, 2019.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Adapted imex numerical methods for reaction-diffusion problems.International journal of circuits, systems and signal processing, 13:507–515, 2019
Reference 13
- Resolution
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 445568e4-3c10-48aa-ae21-d0e5c81f74c0 · outbound
This paper cites A theory of biological pattern formation.Kybernetik, 12:30–39, 1972.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems A theory of biological pattern formation.Kybernetik, 12:30–39, 1972
Reference 14
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8a380587-3f99-4537-b2b8-98ad408d90bd · outbound
This paper cites Springer Science & Business Media, 2006.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Springer Science & Business Media, 2006
Reference 15
- Resolution
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- no resolver link, observed 2026-06-26T07:43:48.390934Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 299926ca-3ec8-4c63-98e7-c50bece48c82 · outbound
This paper cites Exploring spatiotem- poral complexity of a predator-prey system with migration and diffusion by a three-chain coupled map lattice.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Exploring spatiotem- poral complexity of a predator-prey system with migration and diffusion by a three-chain coupled map lattice
Reference 16
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T07:43:48.390934Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6bff73e5-638f-496f-9668-fc4ebf1234bf · outbound
This paper cites Modified patankar linear multistep methods for production-destruction systems.Journal of Scientific Computing, 102(3):87, 2025.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Modified patankar linear multistep methods for production-destruction systems.Journal of Scientific Computing, 102(3):87, 2025
Reference 17
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T07:43:48.390934Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f368238d-022c-4971-be4c-2536c93b9c13 · outbound
This paper cites Stability of multidimensional scalar and matrix polynomials.Proceedings of the IEEE, 66(9):1018–1047, 1978.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Stability of multidimensional scalar and matrix polynomials.Proceedings of the IEEE, 66(9):1018–1047, 1978
Reference 18
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T07:43:48.390934Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a76d7cb0-d21e-47fd-9486-ab1d7f0a64bf · outbound
This paper cites an unresolved cited work.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Unresolved cited work
Reference 19
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T07:43:48.390934Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ee287e01-e3a0-42d6-932f-ac4ad9149211 · outbound
This paper cites Turing instabilities are not enough to ensure pattern formation.Bulletin of mathematical biology, 86(2):21, 2024.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Turing instabilities are not enough to ensure pattern formation.Bulletin of mathematical biology, 86(2):21, 2024
Reference 20
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T07:43:48.390934Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ae517982-0602-41bb-a4e0-cb07a09d3584 · outbound
This paper cites Geco: Geometric conservative nonstandard schemes for biochemical systems.Applied Numerical Mathematics, 155:38–57, 2020.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Geco: Geometric conservative nonstandard schemes for biochemical systems.Applied Numerical Mathematics, 155:38–57, 2020
Reference 21
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T07:43:48.390934Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4647b4ce-baad-4be9-a0d3-54bfe52df3df · outbound
This paper cites Numerical low-rank approximation of matrix differential equations.Journal of Computational and Applied Mathematics, 340:602– 614, 2018.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Numerical low-rank approximation of matrix differential equations.Journal of Computational and Applied Mathematics, 340:602– 614, 2018
Reference 22
- Resolution
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- no resolver link, observed 2026-06-26T07:43:48.390934Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2e3736a7-b5c3-42ba-aba7-77ffc6b5818d · outbound
This paper cites Patterns in soil organic carbon dy- namics: Integrating microbial activity, chemotaxis and data-driven approaches.Mathematics and Computers in Simulation, 234:86–101, 2025.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Patterns in soil organic carbon dy- namics: Integrating microbial activity, chemotaxis and data-driven approaches.Mathematics and Computers in Simulation, 234:86–101, 2025
Reference 23
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T07:43:48.390934Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7e9236c4-5bc1-4a75-b977-3649c2da8362 · outbound
This paper cites Turing patterns on discrete topologies: from networks to higher-order structures.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Turing patterns on discrete topologies: from networks to higher-order structures
Reference 24
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T07:43:48.390934Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 16facdf1-d0af-4895-9ccd-cf54abeba563 · outbound
This paper cites Mathematical biology II: spatial models and biomedical applications.Interdisciplinary Applied Mathematics, 18, 2003.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Mathematical biology II: spatial models and biomedical applications.Interdisciplinary Applied Mathematics, 18, 2003
Reference 25
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T07:43:48.390934Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ae7abad8-8502-45a9-a8ee-798a09fd74a6 · outbound
This paper cites A determinant criterion for stability analysis and design of linear discrete systems.Technical Gazette, 22(6):1511–1516, 2015.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems A determinant criterion for stability analysis and design of linear discrete systems.Technical Gazette, 22(6):1511–1516, 2015
Reference 26
- Resolution
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- no resolver link, observed 2026-06-26T07:43:48.390934Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5fc4d22c-9aae-46b4-83f3-f2b273fa0246 · outbound
This paper cites Implicit-explicit methods for reaction-diffusion problems in pattern formation.Journal of Mathematical Biology, 34(2):148–176, 1995.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Implicit-explicit methods for reaction-diffusion problems in pattern formation.Journal of Mathematical Biology, 34(2):148–176, 1995
Reference 27
- Resolution
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- no resolver link, observed 2026-06-26T07:43:48.390934Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9dc56752-7db1-4433-bbc5-b18106ed4be4 · outbound
This paper cites Numerical bifurcation anal- ysis of turing and symmetry broken patterns of a pde model for vegetation dynamics.Journal of Mathematical Biology, 92(5):66, 2026.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Numerical bifurcation anal- ysis of turing and symmetry broken patterns of a pde model for vegetation dynamics.Journal of Mathematical Biology, 92(5):66, 2026
Reference 28
- Resolution
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- no resolver link, observed 2026-06-26T07:43:48.390934Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation da048bb3-aee7-4f62-8ddc-9976982ca480 · outbound
This paper cites The chemical basis of morphogenesis.Philosophical Transactions of the Royal Society of London.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems The chemical basis of morphogenesis.Philosophical Transactions of the Royal Society of London
Reference 29
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation aea63e34-b60d-4fab-9253-ce0831cc8b9c · outbound
This paper cites Visualpde: rapid interactive simulations of partial differential equations.Bulletin of Mathematical Biology, 85(11):113, 2023.
Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems Visualpde: rapid interactive simulations of partial differential equations.Bulletin of Mathematical Biology, 85(11):113, 2023
Reference 30
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Pith citing papers
Observation a656e717-6892-443a-a33b-941c3c356fc1 · inbound
Pattern formation: reactivity is not necessary for chemotaxis--driven instabilities cites this paper.
Pattern formation: reactivity is not necessary for chemotaxis--driven instabilities Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems
Reference 32
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- local_arxiv, observed 2026-08-05T14:51:09.872873Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.