Gandy, Demi L.; Nelson, Martin R. Analyzing pattern formation in the Gray-Scott model: an XPPAUT tutorial. (English) Zbl 1497.92370 SIAM Rev. 64, No. 3, 728-747 (2022). MSC: 92E20 35K57 35B36 92C15 PDF BibTeX XML Cite \textit{D. L. Gandy} and \textit{M. R. Nelson}, SIAM Rev. 64, No. 3, 728--747 (2022; Zbl 1497.92370) Full Text: DOI OpenURL
Jia, Lan; Li, Liang Stability and dynamic transition of vegetation model for flat arid terrains. (English) Zbl 1490.35030 Discrete Contin. Dyn. Syst., Ser. B 27, No. 6, 3375-3398 (2022). MSC: 35B32 35B35 35B09 35K51 35K58 37L10 PDF BibTeX XML Cite \textit{L. Jia} and \textit{L. Li}, Discrete Contin. Dyn. Syst., Ser. B 27, No. 6, 3375--3398 (2022; Zbl 1490.35030) Full Text: DOI OpenURL
Han, Che; Wang, Yu-Lan; Li, Zhi-Yuan A high-precision numerical approach to solving space fractional Gray-Scott model. (English) Zbl 07443237 Appl. Math. Lett. 125, Article ID 107759, 7 p. (2022). MSC: 65M70 35Q55 35R11 35K57 68W30 PDF BibTeX XML Cite \textit{C. Han} et al., Appl. Math. Lett. 125, Article ID 107759, 7 p. (2022; Zbl 07443237) Full Text: DOI OpenURL
Arafa, Anas; Hagag, Ahmed Approximate solutions for some reaction-diffusion systems with non integer order. (English) Zbl 07486463 Int. J. Appl. Comput. Math. 7, No. 1, Paper No. 25, 23 p. (2021). MSC: 65-XX 35-XX PDF BibTeX XML Cite \textit{A. Arafa} and \textit{A. Hagag}, Int. J. Appl. Comput. Math. 7, No. 1, Paper No. 25, 23 p. (2021; Zbl 07486463) Full Text: DOI OpenURL
Song, Fangying; Zhang, Jun; Wang, Jinrong Convergence analysis and error estimate of second-order implicit-explicit scheme for Gray-Scott model. (English) Zbl 1480.65225 Int. J. Comput. Math. 98, No. 11, 2330-2340 (2021). MSC: 65M06 35Q92 65M12 65M15 PDF BibTeX XML Cite \textit{F. Song} et al., Int. J. Comput. Math. 98, No. 11, 2330--2340 (2021; Zbl 1480.65225) Full Text: DOI OpenURL
Hernández-Santamaría, Víctor; Le Balc’h, Kévin Local controllability of the one-dimensional nonlocal Gray-Scott model with moving controls. (English) Zbl 1481.35369 J. Evol. Equ. 21, No. 4, 4539-4574 (2021). MSC: 35R09 35K57 45K05 93B05 93B07 93C20 PDF BibTeX XML Cite \textit{V. Hernández-Santamaría} and \textit{K. Le Balc'h}, J. Evol. Equ. 21, No. 4, 4539--4574 (2021; Zbl 1481.35369) Full Text: DOI arXiv OpenURL
Karaagac, Berat Numerical treatment of Gray-Scott model with operator splitting method. (English) Zbl 1475.65061 Discrete Contin. Dyn. Syst., Ser. S 14, No. 7, 2373-2386 (2021). MSC: 65L60 35Q68 65D07 PDF BibTeX XML Cite \textit{B. Karaagac}, Discrete Contin. Dyn. Syst., Ser. S 14, No. 7, 2373--2386 (2021; Zbl 1475.65061) Full Text: DOI OpenURL
Hepson, Ozlem Ersoy; Yiğit, Gülsemay; Allahviranloo, Tofigh Numerical simulations of reaction-diffusion systems in biological and chemical mechanisms with quartic-trigonometric B-splines. (English) Zbl 1476.92003 Comput. Appl. Math. 40, No. 4, Paper No. 144, 23 p. (2021). MSC: 92-10 65D07 65M70 35K57 92C15 PDF BibTeX XML Cite \textit{O. E. Hepson} et al., Comput. Appl. Math. 40, No. 4, Paper No. 144, 23 p. (2021; Zbl 1476.92003) Full Text: DOI OpenURL
Xiao, Qiaoyi; Li, Chunqiu Invariant Borel probability measures for the discrete three component reversible Gray-Scott model. (Chinese. English summary) Zbl 1488.37062 Acta Math. Sci., Ser. A, Chin. Ed. 41, No. 2, 523-537 (2021). MSC: 37L40 37L30 37L60 PDF BibTeX XML Cite \textit{Q. Xiao} and \textit{C. Li}, Acta Math. Sci., Ser. A, Chin. Ed. 41, No. 2, 523--537 (2021; Zbl 1488.37062) OpenURL
Aljhani, Sami; Noorani, Mohd Salmi Md; Saad, Khaled M.; Alomari, A. K. Numerical solutions of certain new models of the time-fractional Gray-Scott. (English) Zbl 1500.65089 J. Funct. Spaces 2021, Article ID 2544688, 12 p. (2021). MSC: 65M99 65H20 35K57 26A33 35R11 35Q79 PDF BibTeX XML Cite \textit{S. Aljhani} et al., J. Funct. Spaces 2021, Article ID 2544688, 12 p. (2021; Zbl 1500.65089) Full Text: DOI OpenURL
Mesdoui, Fatiha; Shawagfeh, Nabil; Ouannas, Adel Global synchronization of fractional-order and integer-order \(N\) component reaction diffusion systems: application to biochemical models. (English) Zbl 1476.37109 Math. Methods Appl. Sci. 44, No. 1, 1003-1012 (2021). MSC: 37N35 35K57 26A33 34D20 PDF BibTeX XML Cite \textit{F. Mesdoui} et al., Math. Methods Appl. Sci. 44, No. 1, 1003--1012 (2021; Zbl 1476.37109) Full Text: DOI OpenURL
Chen, Ting; Li, Shimin; Llibre, Jaume Phase portraits and bifurcation diagram of the Gray-Scott model. (English) Zbl 1462.34075 J. Math. Anal. Appl. 496, No. 2, Article ID 124840, 28 p. (2021). MSC: 34C60 92C45 34C05 34C23 PDF BibTeX XML Cite \textit{T. Chen} et al., J. Math. Anal. Appl. 496, No. 2, Article ID 124840, 28 p. (2021; Zbl 1462.34075) Full Text: DOI OpenURL
Arafa, Anas A different approach for conformable fractional biochemical reaction-diffusion models. (English) Zbl 1474.35605 Appl. Math., Ser. B (Engl. Ed.) 35, No. 4, 452-467 (2020). MSC: 35Q92 92C45 PDF BibTeX XML Cite \textit{A. Arafa}, Appl. Math., Ser. B (Engl. Ed.) 35, No. 4, 452--467 (2020; Zbl 1474.35605) Full Text: DOI OpenURL
Liu, Yang; Fan, Enyu; Yin, Baoli; Li, Hong; Wang, Jinfeng TT-M finite element algorithm for a two-dimensional space fractional Gray-Scott model. (English) Zbl 1451.65150 Comput. Math. Appl. 80, No. 7, 1793-1809 (2020). MSC: 65M60 34K37 65M15 35Q79 65M22 65H10 PDF BibTeX XML Cite \textit{Y. Liu} et al., Comput. Math. Appl. 80, No. 7, 1793--1809 (2020; Zbl 1451.65150) Full Text: DOI OpenURL
Xie, Wen-Xian; Cao, Shu-Ping; Cai, Li; Zhang, Xiao-Xuan Study on Turing patterns of Gray-Scott model via amplitude equation. (English) Zbl 1448.92404 Int. J. Bifurcation Chaos Appl. Sci. Eng. 30, No. 8, Article ID 2050121, 19 p. (2020). MSC: 92E20 35B32 35K57 PDF BibTeX XML Cite \textit{W.-X. Xie} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 30, No. 8, Article ID 2050121, 19 p. (2020; Zbl 1448.92404) Full Text: DOI OpenURL
Bhatt, H. P.; Khaliq, A. Q. M.; Furati, K. M. Efficient high-order compact exponential time differencing method for space-fractional reaction-diffusion systems with nonhomogeneous boundary conditions. (English) Zbl 1437.65089 Numer. Algorithms 83, No. 4, 1373-1397 (2020). MSC: 65M06 65F05 26A33 35R11 35K57 80A32 35Q79 65M12 65M15 PDF BibTeX XML Cite \textit{H. P. Bhatt} et al., Numer. Algorithms 83, No. 4, 1373--1397 (2020; Zbl 1437.65089) Full Text: DOI OpenURL
Wang, Jingjing; Jia, Yunfeng Analysis on bifurcation and stability of a generalized Gray-Scott chemical reaction model. (English) Zbl 07568478 Physica A 528, Article ID 121394, 11 p. (2019). MSC: 82-XX 37M20 58J55 35K57 PDF BibTeX XML Cite \textit{J. Wang} and \textit{Y. Jia}, Physica A 528, Article ID 121394, 11 p. (2019; Zbl 07568478) Full Text: DOI OpenURL
Zhang, Shimei; Sun, Yao; Min, Tao Numerical solution of reaction-diffusion model in the biological pattern and its parameters inversion. (Chinese. English summary) Zbl 1449.65268 Math. Pract. Theory 49, No. 21, 206-212 (2019). MSC: 65M60 65M32 92C15 35K57 PDF BibTeX XML Cite \textit{S. Zhang} et al., Math. Pract. Theory 49, No. 21, 206--212 (2019; Zbl 1449.65268) OpenURL
Tok-Onarcan, Aysun; Adar, Nihat; Dag, Idiris Wave simulations of Gray-Scott reaction-diffusion system. (English) Zbl 1427.65137 Math. Methods Appl. Sci. 42, No. 16, 5566-5581 (2019). MSC: 65L60 35K57 42A10 65D07 PDF BibTeX XML Cite \textit{A. Tok-Onarcan} et al., Math. Methods Appl. Sci. 42, No. 16, 5566--5581 (2019; Zbl 1427.65137) Full Text: DOI OpenURL
Al-Hdaibat, B.; Naser, M. F. M.; Safi, M. A. Degenerate Bogdanov-Takens bifurcations in the Gray-Scott model. (English) Zbl 1428.34051 Nonlinear Dyn. Syst. Theory 19, No. 2, 253-262 (2019). MSC: 34C23 35C07 34C45 34C20 34C05 PDF BibTeX XML Cite \textit{B. Al-Hdaibat} et al., Nonlinear Dyn. Syst. Theory 19, No. 2, 253--262 (2019; Zbl 1428.34051) OpenURL
Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F. A numerical solution for a variable-order reaction-diffusion model by using fractional derivatives with non-local and non-singular kernel. (English) Zbl 07547497 Physica A 491, 406-424 (2018). MSC: 82-XX PDF BibTeX XML Cite \textit{A. Coronel-Escamilla} et al., Physica A 491, 406--424 (2018; Zbl 07547497) Full Text: DOI OpenURL
Gandhi, Punit; Zelnik, Yuval R.; Knobloch, Edgar Spatially localized structures in the Gray-Scott model. (English) Zbl 1425.35099 Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 376, No. 2135, Article ID 20170375, 20 p. (2018). MSC: 35K57 35K40 65P40 35Q92 PDF BibTeX XML Cite \textit{P. Gandhi} et al., Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 376, No. 2135, Article ID 20170375, 20 p. (2018; Zbl 1425.35099) Full Text: DOI OpenURL
Zheng, Zhi; Chen, Xinfu; Qi, Yuanwei; Zhou, Shulin Existence of traveling waves of general Gray-Scott models. (English) Zbl 1439.34033 J. Dyn. Differ. Equations 30, No. 4, 1469-1487 (2018). Reviewer: Ramzi S. Alsaedi (Jeddah) MSC: 34B40 34C37 92E20 35C07 PDF BibTeX XML Cite \textit{Z. Zheng} et al., J. Dyn. Differ. Equations 30, No. 4, 1469--1487 (2018; Zbl 1439.34033) Full Text: DOI OpenURL
Qi, Yuanwei; Zhu, Yi The travelling wave of gray-Scott systems – existence, multiplicity and stability. (English) Zbl 1448.92400 J. Biol. Dyn. 11, Suppl. 2, 379-399 (2017). MSC: 92E20 35C07 35K57 PDF BibTeX XML Cite \textit{Y. Qi} and \textit{Y. Zhu}, J. Biol. Dyn. 11, 379--399 (2017; Zbl 1448.92400) Full Text: DOI OpenURL
Kalita, Jiten C. A dual-purpose high order compact approach for pattern formation using gray-Scott model. (English) Zbl 1397.76094 Int. J. Appl. Comput. Math. 3, No. 3, 2747-2760 (2017). MSC: 76M20 65N06 65Z05 76D05 97M60 35K57 92C15 92C35 PDF BibTeX XML Cite \textit{J. C. Kalita}, Int. J. Appl. Comput. Math. 3, No. 3, 2747--2760 (2017; Zbl 1397.76094) Full Text: DOI OpenURL
Delgado, Joaquín; Hernández-Martínez, Lucía Ivonne; Pérez-López, Javier Global bifurcation map of the homogeneous states in the Gray-Scott model. (English) Zbl 1370.34084 Int. J. Bifurcation Chaos Appl. Sci. Eng. 27, No. 7, Article ID 1730024, 16 p. (2017). MSC: 34C60 92C45 34C05 34D20 34C23 PDF BibTeX XML Cite \textit{J. Delgado} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 27, No. 7, Article ID 1730024, 16 p. (2017; Zbl 1370.34084) Full Text: DOI arXiv OpenURL
Dehghan, Mehdi; Abbaszadeh, Mostafa Numerical study of three-dimensional Turing patterns using a meshless method based on moving Kriging element free Galerkin (EFG) approach. (English) Zbl 1359.65199 Comput. Math. Appl. 72, No. 3, 427-454 (2016). MSC: 65M60 65M20 65M70 92C15 PDF BibTeX XML Cite \textit{M. Dehghan} and \textit{M. Abbaszadeh}, Comput. Math. Appl. 72, No. 3, 427--454 (2016; Zbl 1359.65199) Full Text: DOI OpenURL
Qi, Yuanwei The traveling wave of auto-catalytic systems – monotone and multi-peak solutions. (English) Zbl 1363.35178 J. Math. Study 49, No. 2, 149-168 (2016). MSC: 35K57 35A18 92E20 PDF BibTeX XML Cite \textit{Y. Qi}, J. Math. Study 49, No. 2, 149--168 (2016; Zbl 1363.35178) Full Text: DOI Link OpenURL
Bhatt, H. P.; Khaliq, A. Q. M. A compact fourth-order \(L\)-stable scheme for reaction-diffusion systems with nonsmooth data. (English) Zbl 1382.65234 J. Comput. Appl. Math. 299, 176-193 (2016). MSC: 65M06 65L06 65M20 PDF BibTeX XML Cite \textit{H. P. Bhatt} and \textit{A. Q. M. Khaliq}, J. Comput. Appl. Math. 299, 176--193 (2016; Zbl 1382.65234) Full Text: DOI OpenURL
Zhang, Rongpei; Zhu, Jiang; Loula, Abimael F. D.; Yu, Xijun A new nonlinear Galerkin finite element method for the computation of reaction diffusion equations. (English) Zbl 1329.65232 J. Math. Anal. Appl. 434, No. 1, 136-148 (2016). MSC: 65M60 35K57 PDF BibTeX XML Cite \textit{R. Zhang} et al., J. Math. Anal. Appl. 434, No. 1, 136--148 (2016; Zbl 1329.65232) Full Text: DOI OpenURL
Owolabi, Kolade M. Robust IMEX schemes for solving two-dimensional reaction-diffusion models. (English) Zbl 1401.65100 Int. J. Nonlinear Sci. Numer. Simul. 16, No. 6, 271-284 (2015). MSC: 65M20 35K57 35K20 35K58 65M06 76R50 92C15 PDF BibTeX XML Cite \textit{K. M. Owolabi}, Int. J. Nonlinear Sci. Numer. Simul. 16, No. 6, 271--284 (2015; Zbl 1401.65100) Full Text: DOI OpenURL
Zhang, Kexue; Liu, Xinzhi; Xie, Wei-Chau Impulsive control and synchronization of spatiotemporal chaos in the Gray-Scott model. (English) Zbl 1327.93232 Cojocaru, Monica G. (ed.) et al., Interdisciplinary topics in applied mathematics, modeling and computational science. Selected papers based on the presentations at the 2nd conference, AMMCS 2013, Waterloo, Canada, August 26–30, 2013. Cham: Springer (ISBN 978-3-319-12306-6/hbk; 978-3-319-12307-3/ebook). Springer Proceedings in Mathematics & Statistics 117, 549-555 (2015). MSC: 93C20 35R12 93D05 PDF BibTeX XML Cite \textit{K. Zhang} et al., Springer Proc. Math. Stat. 117, 549--555 (2015; Zbl 1327.93232) Full Text: DOI OpenURL
Kuznetsov, Yu. A.; Meijer, H. G. E.; Al-Hdaibat, B.; Govaerts, W. Accurate approximation of homoclinic solutions in Gray-Scott kinetic model. (English) Zbl 1325.34063 Int. J. Bifurcation Chaos Appl. Sci. Eng. 25, No. 9, Article ID 1550125, 10 p. (2015). MSC: 34C60 34C37 34C23 34C20 65L99 PDF BibTeX XML Cite \textit{Yu. A. Kuznetsov} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 25, No. 9, Article ID 1550125, 10 p. (2015; Zbl 1325.34063) OpenURL
Matsuya, Keisuke; Murata, Mikio Spatial pattern of discrete and ultradiscrete Gray-Scott model. (English) Zbl 1302.39014 Discrete Contin. Dyn. Syst., Ser. B 20, No. 1, 173-187 (2015). MSC: 39A12 35K57 PDF BibTeX XML Cite \textit{K. Matsuya} and \textit{M. Murata}, Discrete Contin. Dyn. Syst., Ser. B 20, No. 1, 173--187 (2015; Zbl 1302.39014) Full Text: DOI arXiv OpenURL
Owolabi, Kolade M.; Patidar, Kailash C. Numerical solution of singular patterns in one-dimensional Gray-Scott-like models. (English) Zbl 1401.65101 Int. J. Nonlinear Sci. Numer. Simul. 15, No. 7-8, 437-462 (2014). MSC: 65M20 65M70 92-08 35K40 35K57 76R50 PDF BibTeX XML Cite \textit{K. M. Owolabi} and \textit{K. C. Patidar}, Int. J. Nonlinear Sci. Numer. Simul. 15, No. 7--8, 437--462 (2014; Zbl 1401.65101) Full Text: DOI OpenURL
Bueno-Orovio, Alfonso; Kay, David; Burrage, Kevin Fourier spectral methods for fractional-in-space reaction-diffusion equations. (English) Zbl 1306.65265 BIT 54, No. 4, 937-954 (2014). MSC: 65M70 35K57 35R11 PDF BibTeX XML Cite \textit{A. Bueno-Orovio} et al., BIT 54, No. 4, 937--954 (2014; Zbl 1306.65265) Full Text: DOI Link OpenURL
Meyries, M.; Rademacher, J. D. M.; Siero, E. Quasi-linear parabolic reaction-diffusion systems: a user’s guide to well-posedness, spectra, and stability of travelling waves. (English) Zbl 1297.35110 SIAM J. Appl. Dyn. Syst. 13, No. 1, 249-275 (2014). MSC: 35K57 35K59 35C07 35B35 35B36 PDF BibTeX XML Cite \textit{M. Meyries} et al., SIAM J. Appl. Dyn. Syst. 13, No. 1, 249--275 (2014; Zbl 1297.35110) Full Text: DOI arXiv OpenURL
Murata, Mikio Discretization and ultradiscretization of non-integrable systems. (Japanese. English summary) Zbl 1303.39006 RIMS Kôkyûroku Bessatsu B41, 85-99 (2013). MSC: 39A14 68Q80 37B15 37L60 PDF BibTeX XML Cite \textit{M. Murata}, RIMS Kôkyûroku Bessatsu B41, 85--99 (2013; Zbl 1303.39006) OpenURL
Hansen, Eskil; Henningsson, Erik A convergence analysis of the Peaceman-Rachford scheme for semilinear evolution equations. (English) Zbl 1278.65077 SIAM J. Numer. Anal. 51, No. 4, 1900-1910 (2013). Reviewer: Qin Meng Zhao (Beijing) MSC: 65J08 35K57 65M12 47H06 34G20 82C26 PDF BibTeX XML Cite \textit{E. Hansen} and \textit{E. Henningsson}, SIAM J. Numer. Anal. 51, No. 4, 1900--1910 (2013; Zbl 1278.65077) Full Text: DOI arXiv OpenURL
Notsu, Hirofumi; Ueyama, Daishin; Yamaguchi, Masahiro A self-organized mesh generator using pattern formation in a reaction-diffusion system. (English) Zbl 1256.65088 Appl. Math. Lett. 26, No. 2, 201-206 (2013). MSC: 65M50 65M06 35K57 PDF BibTeX XML Cite \textit{H. Notsu} et al., Appl. Math. Lett. 26, No. 2, 201--206 (2013; Zbl 1256.65088) Full Text: DOI OpenURL
Jia, Xiaolin; Zhao, Caidi; Yang, Xinbo Global attractor and Kolmogorov entropy of three component reversible Gray-Scott model on infinite lattices. (English) Zbl 1264.34018 Appl. Math. Comput. 218, No. 19, 9781-9789 (2012). Reviewer: Peixuan Weng (Guangzhou) MSC: 34A33 34D45 34D05 37A35 PDF BibTeX XML Cite \textit{X. Jia} et al., Appl. Math. Comput. 218, No. 19, 9781--9789 (2012; Zbl 1264.34018) Full Text: DOI OpenURL
Doelman, Arjen; Rademacher, Jens D. M.; van der Stelt, Sjors Hopf dances near the tips of Busse balloons. (English) Zbl 1252.35032 Discrete Contin. Dyn. Syst., Ser. S 5, No. 1, 61-92 (2012). Reviewer: Denise Huet (Nancy) MSC: 35B25 35K57 37L15 34L16 35B36 35K45 35K58 PDF BibTeX XML Cite \textit{A. Doelman} et al., Discrete Contin. Dyn. Syst., Ser. S 5, No. 1, 61--92 (2012; Zbl 1252.35032) Full Text: DOI Link OpenURL
Mach, Jan Application of the nonlinear Galerkin FEM method to the solution of the reaction diffusion equations. (English) Zbl 1262.65132 J. Math-for-Ind. 2011, Spec. Issue, 41-51 (2011). MSC: 65M60 35K20 PDF BibTeX XML Cite \textit{J. Mach}, J. Math-for-Ind. 2011, 41--51 (2011; Zbl 1262.65132) Full Text: Link OpenURL
Mahara, Hitoshi; Yamaguchi, Tomohiko Calculation of the entropy balance equation in a non-equilibrium reaction-diffusion system. (English) Zbl 1229.82105 Entropy 12, No. 12, 2436-2449 (2010). MSC: 82C03 35K57 PDF BibTeX XML Cite \textit{H. Mahara} and \textit{T. Yamaguchi}, Entropy 12, No. 12, 2436--2449 (2010; Zbl 1229.82105) Full Text: DOI OpenURL
Wei, Juncheng; Winter, Matthias Stability of spiky solutions in a reaction-diffusion system with four morphogens on the real line. (English) Zbl 1225.35025 SIAM J. Math. Anal. 42, No. 6, 2818-2841 (2010). Reviewer: Jiaqi Mo (Wuhu) MSC: 35B35 92C40 35K57 35K51 35K58 35B36 PDF BibTeX XML Cite \textit{J. Wei} and \textit{M. Winter}, SIAM J. Math. Anal. 42, No. 6, 2818--2841 (2010; Zbl 1225.35025) Full Text: DOI OpenURL
Mahara, Hitoshi; Yamaguchi, Tomohiko Entropy balance in distributed reversible Gray-Scott model. (English) Zbl 1211.37032 Physica D 239, No. 11, 729-734 (2010). Reviewer: Yuang-Ling Ye (Guangzhou) MSC: 37D35 35K57 37D45 PDF BibTeX XML Cite \textit{H. Mahara} and \textit{T. Yamaguchi}, Physica D 239, No. 11, 729--734 (2010; Zbl 1211.37032) Full Text: DOI OpenURL
Peng, R.; Wang, M. X. Some nonexistence results for nonconstant stationary solutions to the Gray-Scott model in a bounded domain. (English) Zbl 1173.35452 Appl. Math. Lett. 22, No. 4, 569-573 (2009). MSC: 35J55 35Q80 PDF BibTeX XML Cite \textit{R. Peng} and \textit{M. X. Wang}, Appl. Math. Lett. 22, No. 4, 569--573 (2009; Zbl 1173.35452) Full Text: DOI OpenURL
Zhang, Kai; Wong, Jeff C.-F.; Zhang, Ran Second-order implicit-explicit scheme for the Gray-Scott model. (English) Zbl 1135.65377 J. Comput. Appl. Math. 213, No. 2, 559-581 (2008). MSC: 65M60 35K57 80A32 35Q72 65M15 PDF BibTeX XML Cite \textit{K. Zhang} et al., J. Comput. Appl. Math. 213, No. 2, 559--581 (2008; Zbl 1135.65377) Full Text: DOI OpenURL
Wacher, A.; Sobey, I. String gradient weighted moving finite elements in multiple dimensions with applications in two dimensions. (English) Zbl 1134.76034 SIAM J. Sci. Comput. 29, No. 2, 459-480 (2007). MSC: 76M10 76S05 76V05 65M60 65M50 PDF BibTeX XML Cite \textit{A. Wacher} and \textit{I. Sobey}, SIAM J. Sci. Comput. 29, No. 2, 459--480 (2007; Zbl 1134.76034) Full Text: DOI Link OpenURL
Nishiura, Yasumasa; Oyama, Yoshihito; Ueda, Kei-ichi Dynamics of traveling pulses in heterogeneous media of jump type. (English) Zbl 1145.35021 Hokkaido Math. J. 36, No. 1, 207-242 (2007). Reviewer: Alois Steindl (Wien) MSC: 35B32 35K57 34C37 PDF BibTeX XML Cite \textit{Y. Nishiura} et al., Hokkaido Math. J. 36, No. 1, 207--242 (2007; Zbl 1145.35021) Full Text: DOI OpenURL
Peng, Rui; Wang, Ming-xin On pattern formation in the Gray-Scott model. (English) Zbl 1143.35318 Sci. China, Ser. A 50, No. 3, 377-386 (2007). MSC: 35J55 35B45 92C15 92C40 PDF BibTeX XML Cite \textit{R. Peng} and \textit{M.-x. Wang}, Sci. China, Ser. A 50, No. 3, 377--386 (2007; Zbl 1143.35318) Full Text: DOI OpenURL
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng Slow translational instabilities of spike patterns in the one-dimensional Gray-Scott model. (English) Zbl 1105.35132 Interfaces Free Bound. 8, No. 2, 185-222 (2006). Reviewer: Yuri V. Rogovchenko (Famagusta) MSC: 35Q80 92C15 35K60 35B35 PDF BibTeX XML Cite \textit{T. Kolokolnikov} et al., Interfaces Free Bound. 8, No. 2, 185--222 (2006; Zbl 1105.35132) Full Text: DOI OpenURL
Awazu, Akinori; Kaneko, Kunihiko Pulse replications and spatially differentiated structure formation in one-dimensional lattice dynamical system. (English) Zbl 1093.92001 Math. Biosci. 201, No. 1-2, 90-100 (2006). MSC: 92B05 37N25 PDF BibTeX XML Cite \textit{A. Awazu} and \textit{K. Kaneko}, Math. Biosci. 201, No. 1--2, 90--100 (2006; Zbl 1093.92001) Full Text: DOI OpenURL
Kolokolnikov, T.; Wei, J. On ring-like solutions for the Gray-Scott model: existence, instability and self-replicating rings. (English) Zbl 1085.35019 Eur. J. Appl. Math. 16, No. 2, 201-237 (2005). Reviewer: Denise Huet (Nancy) MSC: 35B25 35K57 35B35 35K45 35K50 PDF BibTeX XML Cite \textit{T. Kolokolnikov} and \textit{J. Wei}, Eur. J. Appl. Math. 16, No. 2, 201--237 (2005; Zbl 1085.35019) Full Text: DOI OpenURL
McGough, Jeff S.; Riley, Kyle L. A priori bounds for reaction-diffusion systems arising in chemical and biological dynamics. (English) Zbl 1073.35107 Appl. Math. Comput. 163, No. 1, 1-16 (2005). Reviewer: Dirk Horstmann (Köln) MSC: 35K50 92D25 80A30 PDF BibTeX XML Cite \textit{J. S. McGough} and \textit{K. L. Riley}, Appl. Math. Comput. 163, No. 1, 1--16 (2005; Zbl 1073.35107) Full Text: DOI OpenURL
Ai, Shangbing Homoclinic solutions to the Gray-Scott model. (English) Zbl 1122.37305 Appl. Math. Lett. 17, No. 12, 1357-1361 (2004). MSC: 37C29 34C37 PDF BibTeX XML Cite \textit{S. Ai}, Appl. Math. Lett. 17, No. 12, 1357--1361 (2004; Zbl 1122.37305) Full Text: DOI OpenURL
Wei, Juncheng; Winter, Matthias A nonlocal eigenvalue problem and the stability of spikes for reaction-diffusion systems with fractional reaction rates. (English) Zbl 1065.35041 Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, No. 6, 1529-1543 (2003). Reviewer: Boris A. Malomed (Tel Aviv) MSC: 35B25 35K57 35K50 92C15 PDF BibTeX XML Cite \textit{J. Wei} and \textit{M. Winter}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, No. 6, 1529--1543 (2003; Zbl 1065.35041) Full Text: DOI OpenURL
Takagi, Hiroaki; Kaneko, Kunihiko Pattern dynamics of a multi-component reaction-diffusion system: differentiation of replicating spots. (English) Zbl 1042.35029 Int. J. Bifurcation Chaos Appl. Sci. Eng. 12, No. 11, 2579-2598 (2002). MSC: 35K57 35B05 92E20 PDF BibTeX XML Cite \textit{H. Takagi} and \textit{K. Kaneko}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 12, No. 11, 2579--2598 (2002; Zbl 1042.35029) Full Text: DOI OpenURL
Curtu, Rodica Dynamics and bifurcations for the Gray-Scott model with uncatalyzed conversion. (Dinamica şi bifurcaţiile modelului Gray-Scott în prezenţa conversiei necatalizate.) (Romanian) Zbl 1031.37073 Braşov: Editura Universitǎţii Transilvania din Braşov. 240 p. (2002). Reviewer: Adriana Buică (Bellaterra) MSC: 37N35 34C60 37-02 37G99 92E20 PDF BibTeX XML Cite \textit{R. Curtu}, Dinamica şi bifurcaţiile modelului Gray-Scott în prezenţa conversiei necatalizate (Romanian). Braşov: Editura Universitǎţii Transilvania din Braşov (2002; Zbl 1031.37073) OpenURL
Malchow, Horst; Petrovskii, S. V. Dynamical stabilization of an unstable equilibrium in chemical and biological systems. (English) Zbl 1021.92026 Math. Comput. Modelling 36, No. 3, 307-319 (2002). MSC: 92D25 92E20 92D40 35K57 35Q92 37N25 PDF BibTeX XML Cite \textit{H. Malchow} and \textit{S. V. Petrovskii}, Math. Comput. Modelling 36, No. 3, 307--319 (2002; Zbl 1021.92026) Full Text: DOI OpenURL
Marchant, T. R. Cubic autocatalytic reaction-diffusion equations: Semi-analytical solutions. (English) Zbl 1153.35348 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 458, No. 2020, 873-888 (2002). MSC: 35K57 34C23 35K50 92E20 PDF BibTeX XML Cite \textit{T. R. Marchant}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 458, No. 2020, 873--888 (2002; Zbl 1153.35348) Full Text: DOI OpenURL
Leppänen, Teemu; Karttunen, Mikko; Kaski, Kimmo; Barrio, Rafael A.; Zhang, Limei A new dimension to Turing patterns. (English) Zbl 1007.35037 Physica D 168-169, 35-44 (2002). Reviewer: Zhang Whanguo (Shanghai) MSC: 35K57 35B25 PDF BibTeX XML Cite \textit{T. Leppänen} et al., Physica D 168--169, 35--44 (2002; Zbl 1007.35037) Full Text: DOI arXiv OpenURL
Wei, Juncheng; Winter, Matthias Critical threshold and stability of cluster solutions for large reaction-diffusion systems in \(\mathbb{R}^1\). (English) Zbl 1019.35014 SIAM J. Math. Anal. 33, No. 5, 1058-1089 (2002). Reviewer: Michael Grinfeld (Glasgow) MSC: 35B35 35K57 35B40 92C40 PDF BibTeX XML Cite \textit{J. Wei} and \textit{M. Winter}, SIAM J. Math. Anal. 33, No. 5, 1058--1089 (2002; Zbl 1019.35014) Full Text: DOI OpenURL
Nishiura, Yasumasa Global bifurcational approach to the onset of spatio-temporal chaos in reaction diffusion systems. (English) Zbl 1017.35018 Methods Appl. Anal. 8, No. 2, 321-331 (2001). Reviewer: Jesus Hernandez (Madrid) MSC: 35B32 35K57 35K55 35B40 PDF BibTeX XML Cite \textit{Y. Nishiura}, Methods Appl. Anal. 8, No. 2, 321--331 (2001; Zbl 1017.35018) Full Text: DOI OpenURL
Crampin, E. J.; Maini, P. K. Reaction-diffusion models for biological pattern formation. (English) Zbl 1004.92002 Methods Appl. Anal. 8, No. 3, 415-428 (2001). MSC: 92C15 35K57 92C45 35Q92 PDF BibTeX XML Cite \textit{E. J. Crampin} and \textit{P. K. Maini}, Methods Appl. Anal. 8, No. 3, 415--428 (2001; Zbl 1004.92002) Full Text: DOI OpenURL
Rodrigo, M.; Mimura, M. Exact solutions of reaction-diffusion systems and nonlinear wave equations. (English) Zbl 0987.35030 Japan J. Ind. Appl. Math. 18, No. 3, 657-696 (2001). Reviewer: Valery V.Karachik (Tashkent) MSC: 35C05 35Q53 35Q51 35K57 PDF BibTeX XML Cite \textit{M. Rodrigo} and \textit{M. Mimura}, Japan J. Ind. Appl. Math. 18, No. 3, 657--696 (2001; Zbl 0987.35030) Full Text: DOI OpenURL
Muratov, C. B.; Osipov, V. V. Traveling spike autosolitons in the Gray-Scott model. (English) Zbl 0986.34023 Physica D 155, No. 1-2, 112-131 (2001). MSC: 34B40 34E13 34C37 92E20 80A30 80A32 35Q51 PDF BibTeX XML Cite \textit{C. B. Muratov} and \textit{V. V. Osipov}, Physica D 155, No. 1--2, 112--131 (2001; Zbl 0986.34023) Full Text: DOI OpenURL
Ei, Shin-ichiro; Nishiura, Yasumasa; Ueda, Kei-ichi \(2^n\)-splitting or edge-splitting? A manner of splitting in dissipative systems. (English) Zbl 0983.35061 Japan J. Ind. Appl. Math. 18, No. 2, 181-205 (2001). Reviewer: Alois Steindl (Wien) MSC: 35K57 35B32 35B40 35B42 PDF BibTeX XML Cite \textit{S.-i. Ei} et al., Japan J. Ind. Appl. Math. 18, No. 2, 181--205 (2001; Zbl 0983.35061) Full Text: DOI OpenURL
Curtu, Rodica Bifurcation diagram for a dynamical system in enzymology. (English) Zbl 0983.92010 Orman, Gabriel V. (ed.) et al., Proceedings of the 2nd international conference on symmetry and antisymmetry in mathematics, formal languages and computer science, satellite conference of 3ECM, Braşov, Romania, June 29-July 1, 2000. Braşov: Editura Universităţii Transilvania. 121-135 (2000). MSC: 92C45 34C23 37N25 PDF BibTeX XML Cite \textit{R. Curtu}, in: Proceedings of the 2nd international conference on symmetry and antisymmetry in mathematics, formal languages and computer science, satellite conference of 3ECM, Braşov, Romania, June 29--July 1, 2000. Braşov: Editura Universităţii Transilvania. 121--135 (2000; Zbl 0983.92010) OpenURL
Doelman, Arjen; Eckhaus, Wiktor; Kaper, Tasso J. A note on two pulse solutions in the 1-D Gray-Scott model. (English) Zbl 0973.34028 Fiedler, B. (ed.) et al., International conference on differential equations. Proceedings of the conference, Equadiff ’99, Berlin, Germany, August 1-7, 1999. Vol. 1. Singapore: World Scientific. 775-780 (2000). Reviewer: Angela Slavova (Sofia) MSC: 34C15 34C23 PDF BibTeX XML Cite \textit{A. Doelman} et al., in: International conference on differential equations. Proceedings of the conference, Equadiff '99, Berlin, Germany, August 1--7, 1999. Vol. 1. Singapore: World Scientific. 775--780 (2000; Zbl 0973.34028) OpenURL
Nishiura, Yasumasa Complex pulse dynamics in nonlinear dissipative system. (English) Zbl 0976.37045 Fiedler, B. (ed.) et al., International conference on differential equations. Proceedings of the conference, Equadiff ’99, Berlin, Germany, August 1-7, 1999. Vol. 2. Singapore: World Scientific. 1303-1304 (2000). MSC: 37L15 92C15 PDF BibTeX XML Cite \textit{Y. Nishiura}, in: International conference on differential equations. Proceedings of the conference, Equadiff '99, Berlin, Germany, August 1--7, 1999. Vol. 2. Singapore: World Scientific. 1303--1304 (2000; Zbl 0976.37045) OpenURL
Hale, J. K.; Peletier, L. A.; Troy, W. C. Exact homoclinic and heteroclinic solutions of the Gray-Scott model for autocatalysis. (English) Zbl 0965.34037 SIAM J. Appl. Math. 61, No. 1, 102-130 (2000). MSC: 34C37 92E20 34A05 34C60 PDF BibTeX XML Cite \textit{J. K. Hale} et al., SIAM J. Appl. Math. 61, No. 1, 102--130 (2000; Zbl 0965.34037) Full Text: DOI OpenURL
Nishiura, Yasumasa; Ueyama, Daishin A skeleton structure of self-replicating dynamics. (English) Zbl 0936.35090 Physica D 130, No. 1-2, 73-104 (1999). Reviewer: Ion Onciulescu (Iaşi) MSC: 35K57 35B32 35B40 35K55 PDF BibTeX XML Cite \textit{Y. Nishiura} and \textit{D. Ueyama}, Physica D 130, No. 1--2, 73--104 (1999; Zbl 0936.35090) Full Text: DOI OpenURL
Hale, J. K.; Peletier, L. A.; Troy, W. C. Stability and instability in the Gray-Scott model: The case of equal diffusivities. (English) Zbl 0936.92034 Appl. Math. Lett. 12, No. 4, 59-65 (1999). MSC: 92E20 35Q92 35K57 35B35 35B40 PDF BibTeX XML Cite \textit{J. K. Hale} et al., Appl. Math. Lett. 12, No. 4, 59--65 (1999; Zbl 0936.92034) Full Text: DOI OpenURL
Ueyama, Daishin Dynamics of self-replicating patterns in the one-dimensional Gray-Scott model. (English) Zbl 0987.34031 Hokkaido Math. J. 28, No. 1, 175-210 (1999). MSC: 34C23 35B32 35K57 37G10 34C30 PDF BibTeX XML Cite \textit{D. Ueyama}, Hokkaido Math. J. 28, No. 1, 175--210 (1999; Zbl 0987.34031) Full Text: DOI OpenURL
Doelman, Arjen; Gardner, Robert A.; Kaper, Tasso J. Stability analysis of singular patterns in the 1D Gray-Scott model: a matched asymptotics approach. (English) Zbl 0943.34039 Physica D 122, No. 1-4, 1-36 (1998). Reviewer: Iulius Grosu (Iaşi) MSC: 34D20 34C37 34E05 34C23 PDF BibTeX XML Cite \textit{A. Doelman} et al., Physica D 122, No. 1--4, 1--36 (1998; Zbl 0943.34039) Full Text: DOI OpenURL
Jones, Ronald E.; Gunaratne, Gemunu H. Characterization of labyrinthine patterns and their evolution. (English) Zbl 0938.82028 J. Stat. Phys. 93, No. 3-4, 427-448 (1998). MSC: 82B44 37A35 PDF BibTeX XML Cite \textit{R. E. Jones} and \textit{G. H. Gunaratne}, J. Stat. Phys. 93, No. 3--4, 427--448 (1998; Zbl 0938.82028) Full Text: DOI OpenURL
Nishiura, Yasumasa; Ueyama, Daishin A hidden bifurcational structure for self-replicating dynamics. (English) Zbl 0907.35013 Nishiura, Y. (ed.) et al., Proceedings of the international conference on asymptotics in nonlinear diffusive systems – towards the understanding of singularities in dissipative structures –, Sendai, Japan, July 28–August 1, 1997. Sendai: Tohoku Univ. Tohoku Math. Publ. 8, 123-138 (1998). Reviewer: A.Steindl (Wien) MSC: 35B32 35K57 35B10 PDF BibTeX XML Cite \textit{Y. Nishiura} and \textit{D. Ueyama}, Tohoku Math. Publ. 8, 123--138 (1998; Zbl 0907.35013) OpenURL
Gardner, Robert A. Spectral analysis of long wavelength periodic waves and applications. (English) Zbl 0883.35055 J. Reine Angew. Math. 491, 149-181 (1997). Reviewer: R.A.Gardner (Amherst) MSC: 35G10 35K25 35P05 35Q53 35Q35 35L65 PDF BibTeX XML Cite \textit{R. A. Gardner}, J. Reine Angew. Math. 491, 149--181 (1997; Zbl 0883.35055) Full Text: DOI Crelle EuDML OpenURL
Rasmussen, K. E.; Mazin, W.; Mosekilde, E.; Dewel, G.; Borckmans, P. Wave-splitting in the bistable Gray-Scott model. (English) Zbl 0881.92038 Int. J. Bifurcation Chaos Appl. Sci. Eng. 6, No. 6, 1077-1092 (1996). MSC: 92E20 65C20 82C99 PDF BibTeX XML Cite \textit{K. E. Rasmussen} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 6, No. 6, 1077--1092 (1996; Zbl 0881.92038) Full Text: DOI OpenURL
Farr, W. W.; Golubitsky, M. Rotating chemical waves in the Gary-Scott model. (English) Zbl 0745.58041 SIAM J. Appl. Math. 52, No. 1, 181-221 (1992). MSC: 37G99 35K57 37G05 35B32 PDF BibTeX XML Cite \textit{W. W. Farr} and \textit{M. Golubitsky}, SIAM J. Appl. Math. 52, No. 1, 181--221 (1992; Zbl 0745.58041) Full Text: DOI OpenURL
Kaas-Petersen, Christian Bi-periodicity in an isothermal autocatalytic reaction-diffusion system. (English) Zbl 0681.65083 J. Comput. Appl. Math. 26, No. 1-2, 187-198 (1989). Reviewer: C.I.Gheorghiu MSC: 65N35 65H10 35K57 80A32 PDF BibTeX XML Cite \textit{C. Kaas-Petersen}, J. Comput. Appl. Math. 26, No. 1--2, 187--198 (1989; Zbl 0681.65083) Full Text: DOI OpenURL