Brown, Christopher; Derks, Gianne; van Heijster, Peter; Lloyd, David J. B. Analysing transitions from a Turing instability to large periodic patterns in a reaction-diffusion system. (English) Zbl 1528.34049 Nonlinearity 36, No. 12, 6839-6878 (2023). MSC: 34E15 34C05 34C20 34C45 34C23 34D20 34C26 35B36 35K57 PDFBibTeX XMLCite \textit{C. Brown} et al., Nonlinearity 36, No. 12, 6839--6878 (2023; Zbl 1528.34049) Full Text: DOI arXiv OA License
Doelman, Arjen Slow localized patterns in singularly perturbed two-component reaction-diffusion equations. (English) Zbl 1492.35019 Nonlinearity 35, No. 7, 3487-3559 (2022). MSC: 35B25 35B35 35B36 35C07 35K57 37C29 34D15 92D40 PDFBibTeX XMLCite \textit{A. Doelman}, Nonlinearity 35, No. 7, 3487--3559 (2022; Zbl 1492.35019) Full Text: DOI arXiv
Shapira, Alon Z.; Uecker, Hannes; Yochelis, Arik Stripes on finite domains: why the zigzag instability is only a partial story. (English) Zbl 1445.35050 Chaos 30, No. 7, 073104, 7 p. (2020). MSC: 35B36 35B35 PDFBibTeX XMLCite \textit{A. Z. Shapira} et al., Chaos 30, No. 7, 073104, 7 p. (2020; Zbl 1445.35050) Full Text: DOI arXiv
Bastiaansen, Robbin; Chirilus-Bruckner, Martina; Doelman, Arjen Pulse solutions for an extended Klausmeier model with spatially varying coefficients. (English) Zbl 1431.35071 SIAM J. Appl. Dyn. Syst. 19, No. 1, 1-57 (2020). MSC: 35K57 35Q92 35B25 35B35 35C20 37B55 92D40 PDFBibTeX XMLCite \textit{R. Bastiaansen} et al., SIAM J. Appl. Dyn. Syst. 19, No. 1, 1--57 (2020; Zbl 1431.35071) Full Text: DOI arXiv
Bastiaansen, Robbin; Doelman, Arjen The dynamics of disappearing pulses in a singularly perturbed reaction-diffusion system with parameters that vary in time and space. (English) Zbl 1448.34096 Physica D 388, 45-72 (2019). MSC: 34C60 92D40 35Q92 35Q86 34A45 34D20 PDFBibTeX XMLCite \textit{R. Bastiaansen} and \textit{A. Doelman}, Physica D 388, 45--72 (2019; Zbl 1448.34096) Full Text: DOI arXiv
Doelman, Arjen; Rademacher, Jens; de Rijk, Björn; Veerman, Frits Destabilization mechanisms of periodic pulse patterns near a homoclinic limit. (English) Zbl 1400.35164 SIAM J. Appl. Dyn. Syst. 17, No. 2, 1833-1890 (2018). MSC: 35K57 35B10 35B35 35B25 35B36 PDFBibTeX XMLCite \textit{A. Doelman} et al., SIAM J. Appl. Dyn. Syst. 17, No. 2, 1833--1890 (2018; Zbl 1400.35164) Full Text: DOI
de Rijk, Björn Spectra and stability of spatially periodic pulse patterns. II: The critical spectral curve. (English) Zbl 1418.35015 SIAM J. Math. Anal. 50, No. 2, 1958-2019 (2018). Reviewer: Denise Huet (Nancy) MSC: 35B10 35B35 35B25 35K57 34L10 PDFBibTeX XMLCite \textit{B. de Rijk}, SIAM J. Math. Anal. 50, No. 2, 1958--2019 (2018; Zbl 1418.35015) Full Text: DOI
Sewalt, Lotte; Doelman, Arjen Spatially periodic multipulse patterns in a generalized Klausmeier-Gray-Scott model. (English) Zbl 1369.34067 SIAM J. Appl. Dyn. Syst. 16, No. 2, 1113-1163 (2017). MSC: 34C37 34C25 35B25 35B35 35B36 35C07 92D40 PDFBibTeX XMLCite \textit{L. Sewalt} and \textit{A. Doelman}, SIAM J. Appl. Dyn. Syst. 16, No. 2, 1113--1163 (2017; Zbl 1369.34067) Full Text: DOI
de Rijk, Björn; Doelman, Arjen; Rademacher, Jens Spectra and stability of spatially periodic pulse patterns: Evans function factorization via Riccati transformation. (English) Zbl 1336.35042 SIAM J. Math. Anal. 48, No. 1, 61-121 (2016). Reviewer: Denise Huet (Nancy) MSC: 35B25 35B35 34C20 34D09 34L10 35B10 35K57 35K40 PDFBibTeX XMLCite \textit{B. de Rijk} et al., SIAM J. Math. Anal. 48, No. 1, 61--121 (2016; Zbl 1336.35042) Full Text: DOI arXiv
Siero, E.; Doelman, A.; Eppinga, M. B.; Rademacher, J. D. M.; Rietkerk, M.; Siteur, K. Striped pattern selection by advective reaction-diffusion systems: resilience of banded vegetation on slopes. (English) Zbl 1374.92167 Chaos 25, No. 3, 036411, 22 p. (2015). MSC: 92D40 35K57 PDFBibTeX XMLCite \textit{E. Siero} et al., Chaos 25, No. 3, 036411, 22 p. (2015; Zbl 1374.92167) Full Text: DOI Link
Doelman, Arjen; Veerman, Frits An explicit theory for pulses in two component, singularly perturbed, reaction-diffusion equations. (English) Zbl 1339.35021 J. Dyn. Differ. Equations 27, No. 3-4, 555-595 (2015). MSC: 35B25 35B36 35K57 PDFBibTeX XMLCite \textit{A. Doelman} and \textit{F. Veerman}, J. Dyn. Differ. Equations 27, No. 3--4, 555--595 (2015; Zbl 1339.35021) Full Text: DOI
Uecker, Hannes; Wetzel, Daniel Numerical results for snaking of patterns over patterns in some 2D Selkov-Schnakenberg reaction-diffusion systems. (English) Zbl 1297.65162 SIAM J. Appl. Dyn. Syst. 13, No. 1, 94-128 (2014). MSC: 65N30 35Q56 35K57 35B36 PDFBibTeX XMLCite \textit{H. Uecker} and \textit{D. Wetzel}, SIAM J. Appl. Dyn. Syst. 13, No. 1, 94--128 (2014; Zbl 1297.65162) Full Text: DOI arXiv
Sherratt, Jonathan A. Numerical continuation of boundaries in parameter space between stable and unstable periodic travelling wave (wavetrain) solutions of partial differential equations. (English) Zbl 1271.65132 Adv. Comput. Math. 39, No. 1, 175-192 (2013). MSC: 65M99 35G61 35B35 35Q92 35K57 PDFBibTeX XMLCite \textit{J. A. Sherratt}, Adv. Comput. Math. 39, No. 1, 175--192 (2013; Zbl 1271.65132) Full Text: DOI
van der Stelt, Sjors; Doelman, Arjen; Hek, Geertje; Rademacher, Jens D. M. Rise and fall of periodic patterns for a generalized Klausmeier-Gray-Scott model. (English) Zbl 1270.35093 J. Nonlinear Sci. 23, No. 1, 39-95 (2013). Reviewer: Boris A. Malomed (Tel Aviv) MSC: 35B36 35K57 35B32 35Q56 PDFBibTeX XMLCite \textit{S. van der Stelt} et al., J. Nonlinear Sci. 23, No. 1, 39--95 (2013; Zbl 1270.35093) Full Text: DOI