Hupkes, H. J.; Van Vleck, E. S. Travelling waves for adaptive grid discretizations of reaction diffusion systems. III: Nonlinear theory. (English) Zbl 07781523 J. Dyn. Differ. Equations 35, No. 4, 2743-2811 (2023). MSC: 34K31 34K16 35K57 47H10 PDFBibTeX XMLCite \textit{H. J. Hupkes} and \textit{E. S. Van Vleck}, J. Dyn. Differ. Equations 35, No. 4, 2743--2811 (2023; Zbl 07781523) Full Text: DOI OA License
Hupkes, H. J.; Van Vleck, E. S. Travelling waves for adaptive grid discretizations of reaction diffusion systems. I: Well-posedness. (English) Zbl 1497.34108 J. Dyn. Differ. Equations 34, No. 2, 1505-1599 (2022). MSC: 34K31 34C37 34E15 35C07 35K57 65M06 PDFBibTeX XMLCite \textit{H. J. Hupkes} and \textit{E. S. Van Vleck}, J. Dyn. Differ. Equations 34, No. 2, 1505--1599 (2022; Zbl 1497.34108) Full Text: DOI
Van Vleck, Erik S.; Zhang, Aijun Transition fronts of Fisher-KPP equations in locally spatially inhomogeneous patchy environments. (English) Zbl 1486.37043 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 217, Article ID 112748, 38 p. (2022). Reviewer: Xiong Li (Beijing) MSC: 37L60 37N25 39A14 34K31 39A12 92D25 92D40 PDFBibTeX XMLCite \textit{E. S. Van Vleck} and \textit{A. Zhang}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 217, Article ID 112748, 38 p. (2022; Zbl 1486.37043) Full Text: DOI arXiv
Hupkes, Hermen Jan; Morelli, Leonardo; Schouten-Straatman, Willem M.; van Vleck, Erik S. Traveling waves and pattern formation for spatially discrete bistable reaction-diffusion equations. (English) Zbl 1447.34001 Bohner, Martin (ed.) et al., Difference equations and discrete dynamical systems with applications. ICDEA 24, Dresden, Germany, May 21–25, 2018. Proceedings of the 24th international conference on difference equations and applications. Cham: Springer. Springer Proc. Math. Stat. 312, 55-112 (2020). MSC: 34-02 34K16 34K10 34K20 35C07 35B36 34K31 PDFBibTeX XMLCite \textit{H. J. Hupkes} et al., Springer Proc. Math. Stat. 312, 55--112 (2020; Zbl 1447.34001) Full Text: DOI
de Leeuw, Bart; Dubinkina, Svetlana; Frank, Jason; Steyer, Andrew; Tu, Xuemin; Van Vleck, Erik Projected shadowing-based data assimilation. (English) Zbl 1406.37060 SIAM J. Appl. Dyn. Syst. 17, No. 4, 2446-2477 (2018). MSC: 37M99 37N99 68P20 PDFBibTeX XMLCite \textit{B. de Leeuw} et al., SIAM J. Appl. Dyn. Syst. 17, No. 4, 2446--2477 (2018; Zbl 1406.37060) Full Text: DOI arXiv
Hupkes, H. J.; Van Vleck, E. S. Travelling waves for complete discretizations of reaction diffusion systems. (English) Zbl 1353.34094 J. Dyn. Differ. Equations 28, No. 3-4, 955-1006 (2016). MSC: 34K31 37L15 35C07 65M06 65M22 34K26 PDFBibTeX XMLCite \textit{H. J. Hupkes} and \textit{E. S. Van Vleck}, J. Dyn. Differ. Equations 28, No. 3--4, 955--1006 (2016; Zbl 1353.34094) Full Text: DOI
Lamb, Charles; Van Vleck, Erik S. Neutral mixed type functional differential equations. (English) Zbl 1401.34090 J. Dyn. Differ. Equations 28, No. 3-4, 763-804 (2016). Reviewer: Miklavž Mastinšek (Maribor) MSC: 34K40 34K30 PDFBibTeX XMLCite \textit{C. Lamb} and \textit{E. S. Van Vleck}, J. Dyn. Differ. Equations 28, No. 3--4, 763--804 (2016; Zbl 1401.34090) Full Text: DOI
Chung, Yu-Min; Steyer, Andrew; Tubbs, Michael; Van Vleck, Erik S.; Vedantam, Mihir Global error analysis and inertial manifold reduction. (English) Zbl 1382.65192 J. Comput. Appl. Math. 307, 204-215 (2016). MSC: 65L05 34C45 65P40 PDFBibTeX XMLCite \textit{Y.-M. Chung} et al., J. Comput. Appl. Math. 307, 204--215 (2016; Zbl 1382.65192) Full Text: DOI arXiv
Van Vleck, Erik S.; Zhang, Aijun Competing interactions and traveling wave solutions in lattice differential equations. (English) Zbl 1331.39005 Commun. Pure Appl. Anal. 15, No. 2, 457-475 (2016). MSC: 39A12 34K31 35K57 37L60 PDFBibTeX XMLCite \textit{E. S. Van Vleck} and \textit{A. Zhang}, Commun. Pure Appl. Anal. 15, No. 2, 457--475 (2016; Zbl 1331.39005) Full Text: DOI arXiv
Hoffman, Aaron; Hupkes, H. J.; van Vleck, E. S. Multi-dimensional stability of waves travelling through rectangular lattices in rational directions. (English) Zbl 1377.34097 Trans. Am. Math. Soc. 367, No. 12, 8757-8808 (2015). MSC: 34K31 34K10 35K57 35C07 35B35 PDFBibTeX XMLCite \textit{A. Hoffman} et al., Trans. Am. Math. Soc. 367, No. 12, 8757--8808 (2015; Zbl 1377.34097) Full Text: DOI arXiv
Vainchtein, Anna; Van Vleck, Erik S.; Zhang, Aijun Propagation of periodic patterns in a discrete system with competing interactions. (English) Zbl 1387.34108 SIAM J. Appl. Dyn. Syst. 14, No. 2, 523-555 (2015). Reviewer: Caidi Zhao (Wenzhou) MSC: 34K31 37L60 34K09 34K10 PDFBibTeX XMLCite \textit{A. Vainchtein} et al., SIAM J. Appl. Dyn. Syst. 14, No. 2, 523--555 (2015; Zbl 1387.34108) Full Text: DOI Link
Menning, Melissa; Van Vleck, Erik S. On the error in approximating stability spectra for discrete dynamical systems. (English) Zbl 1210.65200 Math. Comput. Simul. 81, No. 5, 1006-1016 (2011). MSC: 65P40 37M25 37B25 PDFBibTeX XMLCite \textit{M. Menning} and \textit{E. S. Van Vleck}, Math. Comput. Simul. 81, No. 5, 1006--1016 (2011; Zbl 1210.65200) Full Text: DOI
Liu, Weishi; Van Vleck, Erik S. Exponential dichotomy for asymptotically hyperbolic two-dimensional linear systems. (English) Zbl 1226.34048 J. Dyn. Differ. Equations 22, No. 4, 697-722 (2010). Reviewer: Thomas Hagen (Memphis) MSC: 34D09 34D10 PDFBibTeX XMLCite \textit{W. Liu} and \textit{E. S. Van Vleck}, J. Dyn. Differ. Equations 22, No. 4, 697--722 (2010; Zbl 1226.34048) Full Text: DOI
Liu, Weishi; Van Vleck, Erik Turning points and traveling waves in Fitzhugh–Nagumo type equations. (English) Zbl 1103.34031 J. Differ. Equations 225, No. 2, 381-410 (2006). MSC: 34C37 34E15 35K57 PDFBibTeX XMLCite \textit{W. Liu} and \textit{E. Van Vleck}, J. Differ. Equations 225, No. 2, 381--410 (2006; Zbl 1103.34031) Full Text: DOI
Van Vleck, Erik; Wang, Bixiang Attractors for lattice fitzHugh–Nagumo systems. (English) Zbl 1086.34047 Physica D 212, No. 3-4, 317-336 (2005). MSC: 34D45 34G20 34A35 PDFBibTeX XMLCite \textit{E. Van Vleck} and \textit{B. Wang}, Physica D 212, No. 3--4, 317--336 (2005; Zbl 1086.34047) Full Text: DOI
Elmer, Christopher E.; Van Vleck, Erik S. Anisotropy, propagation failure, and wave speedup in traveling waves of discretizations of a Nagumo PDE. (English) Zbl 1019.65069 J. Comput. Phys. 185, No. 2, 562-582 (2003). Reviewer: Ll.G.Chambers (Bangor) MSC: 65M12 35K57 65M06 PDFBibTeX XMLCite \textit{C. E. Elmer} and \textit{E. S. Van Vleck}, J. Comput. Phys. 185, No. 2, 562--582 (2003; Zbl 1019.65069) Full Text: DOI
Abell, K. A.; Humphries, A. R.; Van Vleck, E. S. Mosaic solutions and entropy for discrete coupled phase-transition equations. (English) Zbl 1002.35058 Physica D 155, No. 3-4, 274-310 (2001). Reviewer: Messoud Efendiev (Berlin) MSC: 35K55 39A12 37L60 35B30 35R10 PDFBibTeX XMLCite \textit{K. A. Abell} et al., Physica D 155, No. 3--4, 274--310 (2001; Zbl 1002.35058) Full Text: DOI
Jennings, Barbara; Van Vleck, Erik S. Mosaic solutions and spatial entropy for a class of neural network models. (English) Zbl 1090.34562 Int. J. Bifurcation Chaos Appl. Sci. Eng. 10, No. 7, 1661-1675 (2000). MSC: 34C60 34D99 92B20 93D05 PDFBibTeX XMLCite \textit{B. Jennings} and \textit{E. S. Van Vleck}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 10, No. 7, 1661--1675 (2000; Zbl 1090.34562) Full Text: DOI
Scales, John A.; Van Vleck, Erik S. Lyapunov exponents and localization in randomly layered media. (English) Zbl 0876.65023 J. Comput. Phys. 133, No. 1, 27-42 (1997). MSC: 65F15 15B52 82C44 65L15 34L40 34D08 PDFBibTeX XMLCite \textit{J. A. Scales} and \textit{E. S. Van Vleck}, J. Comput. Phys. 133, No. 1, 27--42 (1997; Zbl 0876.65023) Full Text: DOI Link