Nadin, Grégoire; Ogier-Denis, Eric; Toledo, Ana I.; Zaag, Hatem A Turing mechanism in order to explain the patchy nature of Crohn’s disease. (English) Zbl 1466.92004 J. Math. Biol. 83, No. 2, Paper No. 12, 17 p. (2021). MSC: 92-10 92C50 35Q92 PDF BibTeX XML Cite \textit{G. Nadin} et al., J. Math. Biol. 83, No. 2, Paper No. 12, 17 p. (2021; Zbl 1466.92004) Full Text: DOI arXiv OpenURL
Wang, Xiaoli; Zhang, Guohong Bifurcation analysis of a general activator-inhibitor model with nonlocal dispersal. (English) Zbl 1466.35022 Discrete Contin. Dyn. Syst., Ser. B 26, No. 8, 4459-4477 (2021). MSC: 35B32 35B35 35B36 35K51 35K57 35R09 37L15 92C15 PDF BibTeX XML Cite \textit{X. Wang} and \textit{G. Zhang}, Discrete Contin. Dyn. Syst., Ser. B 26, No. 8, 4459--4477 (2021; Zbl 1466.35022) Full Text: DOI OpenURL
Chen, Shanshan; Shi, Junping; Zhang, Guohong Spatial pattern formation in activator-inhibitor models with nonlocal dispersal. (English) Zbl 1466.35024 Discrete Contin. Dyn. Syst., Ser. B 26, No. 4, 1843-1866 (2021). MSC: 35B36 35B32 35B35 35K51 35K57 37L15 92C15 PDF BibTeX XML Cite \textit{S. Chen} et al., Discrete Contin. Dyn. Syst., Ser. B 26, No. 4, 1843--1866 (2021; Zbl 1466.35024) Full Text: DOI OpenURL
Kavallaris, Nikos I.; Barreira, Raquel; Madzvamuse, Anotida Dynamics of shadow system of a singular Gierer-Meinhardt system on an evolving domain. (English) Zbl 1462.35033 J. Nonlinear Sci. 31, No. 1, Paper No. 5, 34 p. (2021). MSC: 35B25 35B36 35B44 35K51 35K57 92D25 PDF BibTeX XML Cite \textit{N. I. Kavallaris} et al., J. Nonlinear Sci. 31, No. 1, Paper No. 5, 34 p. (2021; Zbl 1462.35033) Full Text: DOI arXiv OpenURL
Owolabi, Kolade M.; Karaagac, Berat Chaotic and spatiotemporal oscillations in fractional reaction-diffusion system. (English) Zbl 07511207 Chaos Solitons Fractals 141, Article ID 110302, 16 p. (2020). MSC: 34A34 35A05 35K57 65L05 65M06 93C10 PDF BibTeX XML Cite \textit{K. M. Owolabi} and \textit{B. Karaagac}, Chaos Solitons Fractals 141, Article ID 110302, 16 p. (2020; Zbl 07511207) Full Text: DOI OpenURL
Chen, Yan-Yu; Kohsaka, Yoshihito; Ninomiya, Hirokazu Traveling spots and traveling fingers in singular limit problems of reaction-diffusion systems. (English) Zbl 1292.35022 Discrete Contin. Dyn. Syst., Ser. B 19, No. 3, 697-714 (2014). Reviewer: Guo Lin (Lanzhou) MSC: 35B25 35K57 35C07 35R35 35K45 35K58 PDF BibTeX XML Cite \textit{Y.-Y. Chen} et al., Discrete Contin. Dyn. Syst., Ser. B 19, No. 3, 697--714 (2014; Zbl 1292.35022) Full Text: DOI OpenURL
Abdelmalek, Salem; Louafi, Hichem; Youkana, Amar Existence of global solutions for a Gierer-Meinhardt system with three equations. (English) Zbl 1237.35090 Electron. J. Differ. Equ. 2012, Paper No. 55, 8 p. (2012). MSC: 35K57 92C15 PDF BibTeX XML Cite \textit{S. Abdelmalek} et al., Electron. J. Differ. Equ. 2012, Paper No. 55, 8 p. (2012; Zbl 1237.35090) Full Text: arXiv EMIS OpenURL
Nefedov, N. N.; Nikitin, A. G. Boundary and internal layers in the reaction-diffusion problem with a nonlocal inhibitor. (Russian, English) Zbl 1249.35159 Zh. Vychisl. Mat. Mat. Fiz. 51, No. 6, 1081-1090 (2011); translation in Comput. Math. Math. Phys. 51, No. 6, 1011-1018 (2011). MSC: 35K57 PDF BibTeX XML Cite \textit{N. N. Nefedov} and \textit{A. G. Nikitin}, Zh. Vychisl. Mat. Mat. Fiz. 51, No. 6, 1081--1090 (2011; Zbl 1249.35159); translation in Comput. Math. Math. Phys. 51, No. 6, 1011--1018 (2011) Full Text: DOI OpenURL
Suzuki, Kanako; Takagi, Izumi On the role of basic production terms in an activator-inhibitor system modeling biological pattern formation. (English) Zbl 1243.35162 Funkc. Ekvacioj, Ser. Int. 54, No. 2, 237-274 (2011). Reviewer: Jiaqi Mo (Wuhu) MSC: 35Q92 35K51 35K57 92C15 35B40 PDF BibTeX XML Cite \textit{K. Suzuki} and \textit{I. Takagi}, Funkc. Ekvacioj, Ser. Int. 54, No. 2, 237--274 (2011; Zbl 1243.35162) Full Text: DOI OpenURL
Ogawa, Toshiyuki; Okuda, Takashi Bifurcation analysis to Swift-Hohenberg equation with Steklov type boundary conditions. (English) Zbl 1179.35051 Discrete Contin. Dyn. Syst. 25, No. 1, 273-297 (2009). Reviewer: Dmitry Pelinovsky (Hamilton) MSC: 35B32 35K57 37L10 35K58 35K51 35K35 PDF BibTeX XML Cite \textit{T. Ogawa} and \textit{T. Okuda}, Discrete Contin. Dyn. Syst. 25, No. 1, 273--297 (2009; Zbl 1179.35051) Full Text: DOI OpenURL
Miyamoto, Yasuhito An instability criterion for activator-inhibitor systems in a two-dimensional ball. II. (English) Zbl 1155.35386 J. Differ. Equations 239, No. 1, 61-71 (2007). MSC: 35K50 35B35 35K57 PDF BibTeX XML Cite \textit{Y. Miyamoto}, J. Differ. Equations 239, No. 1, 61--71 (2007; Zbl 1155.35386) Full Text: DOI OpenURL
Jiang, Huiqiang; Ni, Weiming A priori estimates of stationary solutions of an activator-inhibitor system. (English) Zbl 1125.35018 Indiana Univ. Math. J. 56, No. 2, 681-732 (2007). Reviewer: Yaping Liu (Pittsburg) MSC: 35B45 35J55 35K57 35B50 92C15 PDF BibTeX XML Cite \textit{H. Jiang} and \textit{W. Ni}, Indiana Univ. Math. J. 56, No. 2, 681--732 (2007; Zbl 1125.35018) Full Text: DOI arXiv OpenURL
Miyamoto, Yasuhito An instability criterion for activator-inhibitor systems in a two-dimensional ball. (English) Zbl 1154.35371 J. Differ. Equations 229, No. 2, 494-508 (2006). Reviewer: Rodica Luca Tudorache (Iaşi) (MR2263564) MSC: 35K50 35B35 35K57 35Q80 37L15 PDF BibTeX XML Cite \textit{Y. Miyamoto}, J. Differ. Equations 229, No. 2, 494--508 (2006; Zbl 1154.35371) Full Text: DOI OpenURL
Ham, Yoonmee An interface problem in an activator-inhibitor system depending on the spatial average of an inhibitor. (English) Zbl 0986.35118 Far East J. Math. Sci. (FJMS) 3, No. 2, 273-286 (2001). Reviewer: René Sperb (Zürich) MSC: 35Q80 92E20 35B32 35B25 35K57 PDF BibTeX XML Cite \textit{Y. Ham}, Far East J. Math. Sci. (FJMS) 3, No. 2, 273--286 (2001; Zbl 0986.35118) OpenURL
Satnoianu, Razvan A.; Menzinger, Michael; Maini, Philip K. Turing instabilities in general systems. (English) Zbl 1002.92002 J. Math. Biol. 41, No. 6, 493-512 (2000). MSC: 92C15 35K57 35B35 PDF BibTeX XML Cite \textit{R. A. Satnoianu} et al., J. Math. Biol. 41, No. 6, 493--512 (2000; Zbl 1002.92002) Full Text: DOI Link OpenURL
García-Ojalvo, J.; Schimansky-Geier, L. Excitable structures in stochastic bistable media. (English) Zbl 0977.82035 J. Stat. Phys. 101, No. 1-2, 473-481 (2000). MSC: 82C31 37N20 PDF BibTeX XML Cite \textit{J. García-Ojalvo} and \textit{L. Schimansky-Geier}, J. Stat. Phys. 101, No. 1--2, 473--481 (2000; Zbl 0977.82035) Full Text: DOI OpenURL
Yanagida, Eiji Reaction-diffusion systems with skew-gradient structure. (English) Zbl 0968.35057 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. 760-765 (2000). MSC: 35K50 35K57 PDF BibTeX XML Cite \textit{E. Yanagida}, in: International conference on differential equations. Proceedings of the conference, Equadiff '99, Berlin, Germany, August 1--7, 1999. Vol. 1. Singapore: World Scientific. 760--765 (2000; Zbl 0968.35057) OpenURL
Eisner, Jan; Kučera, Milan Spatial patterning in reaction-diffusion systems with nonstandard boundary conditions. (English) Zbl 0969.35019 Ramm, A. G. (ed.) et al., Operator theory and its applications. Proceedings of the international conference, Winnipeg, Canada, October 7-11, 1998. Providence, RI: American Mathematical Society (AMS). Fields Inst. Commun. 25, 239-256 (2000). Reviewer: Sebastian Aniţa (Iaşi) MSC: 35B32 35J85 35K57 35J65 92B05 47H04 PDF BibTeX XML Cite \textit{J. Eisner} and \textit{M. Kučera}, in: Operator theory and its applications. Proceedings of the international conference, Winnipeg, Canada, October 7--11, 1998. Providence, RI: American Mathematical Society (AMS). 239--256 (2000; Zbl 0969.35019) OpenURL
Kawaguchi, Satoshi; Mimura, Masayasu Collision of travelling waves in a reaction-diffusion system with global coupling effect. (English) Zbl 0936.35089 SIAM J. Appl. Math. 59, No. 3, 920-941 (1999). Reviewer: Georgii Sviridyuk (Chelyabinsk) MSC: 35K57 35B25 35B32 PDF BibTeX XML Cite \textit{S. Kawaguchi} and \textit{M. Mimura}, SIAM J. Appl. Math. 59, No. 3, 920--941 (1999; Zbl 0936.35089) Full Text: DOI OpenURL
Tapaswi, P. K.; Chattopadhyay, J. Effects of cross-diffusion on an activator and inhibitor model for the emergence of ordered structure during embryogenesis. (English) Zbl 0828.92001 Nonlinear World 2, No. 3, 295-310 (1995). MSC: 92C15 35Q92 35K57 35B35 PDF BibTeX XML Cite \textit{P. K. Tapaswi} and \textit{J. Chattopadhyay}, Nonlinear World 2, No. 3, 295--310 (1995; Zbl 0828.92001) OpenURL
Niedernostheide, F.-J.; Dohmen, R.; Willebrand, H.; Kerner, B. S.; Purwins, H.-G. Transition from pulsating to rocking localized structures in nonlinear dissipative distributive media with global inhibition. (English) Zbl 0791.35137 Physica D 69, No. 3-4, 425-435 (1993). MSC: 35Q60 35K57 92E20 PDF BibTeX XML Cite \textit{F. J. Niedernostheide} et al., Physica D 69, No. 3--4, 425--435 (1993; Zbl 0791.35137) Full Text: DOI OpenURL
Mimura, Masayasu Pattern formation in reaction-diffusion systems. (English) Zbl 0747.92012 Proc. Int. Congr. Math., Kyoto/Japan 1990, Vol. II, 1627-1637 (1991). Reviewer: R.Sperb (Zürich) MSC: 92C15 35Q92 35K57 PDF BibTeX XML Cite \textit{M. Mimura}, in: Proceedings of the international congress of mathematicians (ICM), August 21-29, 1990, Kyoto, Japan. Volume II. Tokyo etc.: Springer-Verlag. 1627--1637 (1991; Zbl 0747.92012) OpenURL
Meinhardt, Hans Tailoring and coupling of reaction-diffusion systems to obtain reproducible complex pattern formation during development of the higher organisms. (English) Zbl 0672.92010 Appl. Math. Comput. 32, No. 2-3, 103-135 (1989). MSC: 92Cxx PDF BibTeX XML Cite \textit{H. Meinhardt}, Appl. Math. Comput. 32, No. 2--3, 103--135 (1989; Zbl 0672.92010) Full Text: DOI OpenURL