Batko, Bogdan; Gameiro, Marcio; Hung, Ying; Kalies, William; Mischaikow, Konstantin; Vieira, Ewerton Identifying nonlinear dynamics with high confidence from sparse data. (English) Zbl 07803212 SIAM J. Appl. Dyn. Syst. 23, No. 1, 383-409 (2024). MSC: 37M10 60G15 37B35 37C25 PDFBibTeX XMLCite \textit{B. Batko} et al., SIAM J. Appl. Dyn. Syst. 23, No. 1, 383--409 (2024; Zbl 07803212) Full Text: DOI arXiv
Pötzsche, Christian Numerical dynamics of integrodifference equations. (English) Zbl 07707127 Numer. Math. 154, No. 1-2, 249-281 (2023). MSC: 65P40 45G15 65R20 37L45 PDFBibTeX XMLCite \textit{C. Pötzsche}, Numer. Math. 154, No. 1--2, 249--281 (2023; Zbl 07707127) Full Text: DOI
Huynh, Huy; Kloeden, Peter E.; Pötzsche, Christian Forward and pullback dynamics of nonautonomous integrodifference equations: basic constructions. (English) Zbl 1495.37025 J. Dyn. Differ. Equations 34, No. 1, 671-699 (2022). MSC: 37C70 37C60 45G15 92D40 PDFBibTeX XMLCite \textit{H. Huynh} et al., J. Dyn. Differ. Equations 34, No. 1, 671--699 (2022; Zbl 1495.37025) Full Text: DOI arXiv
Lessard, Jean-Philippe; James, J. D. Mireles A rigorous implicit \(C^1\) Chebyshev integrator for delay equations. (English) Zbl 1498.65111 J. Dyn. Differ. Equations 33, No. 4, 1959-1988 (2021). MSC: 65L03 65D30 PDFBibTeX XMLCite \textit{J.-P. Lessard} and \textit{J. D. M. James}, J. Dyn. Differ. Equations 33, No. 4, 1959--1988 (2021; Zbl 1498.65111) Full Text: DOI
Kepley, Shane; Mischaikow, Konstantin; Zhang, Lun Computing linear extensions for polynomial posets subject to algebraic constraints. (English) Zbl 1518.14081 SIAM J. Appl. Algebra Geom. 5, No. 2, 388-416 (2021). MSC: 14Q30 37N25 03C10 06A07 PDFBibTeX XMLCite \textit{S. Kepley} et al., SIAM J. Appl. Algebra Geom. 5, No. 2, 388--416 (2021; Zbl 1518.14081) Full Text: DOI arXiv
Aarset, Christian; Pötzsche, Christian Bifurcations in periodic integrodifference equations in \(C(\Omega)\). I: Analytical results and applications. (English) Zbl 1473.37063 Discrete Contin. Dyn. Syst., Ser. B 26, No. 1, 1-60 (2021). Reviewer: Eduardo Cuesta (Valladolid) MSC: 37G15 45G15 39A30 39A28 39A23 92D25 92D40 PDFBibTeX XMLCite \textit{C. Aarset} and \textit{C. Pötzsche}, Discrete Contin. Dyn. Syst., Ser. B 26, No. 1, 1--60 (2021; Zbl 1473.37063) Full Text: DOI arXiv
Aarset, Christian; Pötzsche, Christian Bifurcations in periodic integrodifference equations in \(C(\Omega)\): II. Discrete torus bifurcations. (English) Zbl 1441.39011 Commun. Pure Appl. Anal. 19, No. 4, 1847-1874 (2020). Reviewer: Eszter Gselmann (Debrecen) MSC: 39A28 37G15 39A23 37N25 92D25 PDFBibTeX XMLCite \textit{C. Aarset} and \textit{C. Pötzsche}, Commun. Pure Appl. Anal. 19, No. 4, 1847--1874 (2020; Zbl 1441.39011) Full Text: DOI
Day, Sarah; Frongillo, Rafael Sofic shifts via Conley index theory: computing lower bounds on recurrent dynamics for maps. (English) Zbl 1436.37018 SIAM J. Appl. Dyn. Syst. 18, No. 3, 1610-1642 (2019). Reviewer: Zdzisław Dzedzej (Gdansk) MSC: 37B30 37B10 37B40 37B20 PDFBibTeX XMLCite \textit{S. Day} and \textit{R. Frongillo}, SIAM J. Appl. Dyn. Syst. 18, No. 3, 1610--1642 (2019; Zbl 1436.37018) Full Text: DOI
Hou, Guoliang; Zhang, Shugong An improved verification algorithm for nonlinear systems of equations based on Krawczyk operator. (English) Zbl 1416.65143 J. Comput. Appl. Math. 359, 145-152 (2019). MSC: 65H10 65G20 PDFBibTeX XMLCite \textit{G. Hou} and \textit{S. Zhang}, J. Comput. Appl. Math. 359, 145--152 (2019; Zbl 1416.65143) Full Text: DOI
Bramburger, Jason; Lutscher, Frithjof Analysis of integrodifference equations with a separable dispersal kernel. (English) Zbl 1414.37036 Acta Appl. Math. 161, 127-151 (2019). MSC: 37N25 39A28 39A60 92D25 PDFBibTeX XMLCite \textit{J. Bramburger} and \textit{F. Lutscher}, Acta Appl. Math. 161, 127--151 (2019; Zbl 1414.37036) Full Text: DOI Link
Day, Sarah Dynamics and chaos for maps and the Conley index. (English) Zbl 1405.37017 van den Berg, Jan Bouwe (ed.) et al., Rigorous numerics in dynamics. AMS short course, Seattle, WA, USA, January 4–5, 2016. Lecture notes. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2814-3/hbk; 978-1-4704-4729-8/ebook). Proceedings of Symposia in Applied Mathematics 74, 175-194 (2018). MSC: 37B10 37B30 37B50 PDFBibTeX XMLCite \textit{S. Day}, Proc. Symp. Appl. Math. 74, 175--194 (2018; Zbl 1405.37017) Full Text: DOI
Castelli, Roberto; Gameiro, Marcio; Lessard, Jean-Philippe Rigorous numerics for ill-posed PDEs: periodic orbits in the Boussinesq equation. (English) Zbl 1390.35262 Arch. Ration. Mech. Anal. 228, No. 1, 129-157 (2018). MSC: 35Q35 76B15 35R25 35B10 42A63 65M70 PDFBibTeX XMLCite \textit{R. Castelli} et al., Arch. Ration. Mech. Anal. 228, No. 1, 129--157 (2018; Zbl 1390.35262) Full Text: DOI arXiv
Junge, Oliver; Kevrekidis, Ioannis G. On the sighting of unicorns: a variational approach to computing invariant sets in dynamical systems. (English) Zbl 1390.37140 Chaos 27, No. 6, 063102, 9 p. (2017). MSC: 37M99 37D10 PDFBibTeX XMLCite \textit{O. Junge} and \textit{I. G. Kevrekidis}, Chaos 27, No. 6, 063102, 9 p. (2017; Zbl 1390.37140) Full Text: DOI arXiv Link
Mireles-James, J. D. Fourier-Taylor approximation of unstable manifolds for compact maps: numerical implementation and computer-assisted error bounds. (English) Zbl 1383.37066 Found. Comput. Math. 17, No. 6, 1467-1523 (2017). MSC: 37L65 37C05 34C45 37D10 65P40 PDFBibTeX XMLCite \textit{J. D. Mireles-James}, Found. Comput. Math. 17, No. 6, 1467--1523 (2017; Zbl 1383.37066) Full Text: DOI
Figueras, Jordi-Lluís; Gameiro, Marcio; Lessard, Jean-Philippe; de la Llave, Rafael A framework for the numerical computation and a posteriori verification of invariant objects of evolution equations. (English) Zbl 1370.65046 SIAM J. Appl. Dyn. Syst. 16, No. 2, 1070-1088 (2017). MSC: 65M22 35K55 37C27 65G40 65F08 PDFBibTeX XMLCite \textit{J.-L. Figueras} et al., SIAM J. Appl. Dyn. Syst. 16, No. 2, 1070--1088 (2017; Zbl 1370.65046) Full Text: DOI arXiv
Lessard, Jean-Philippe; Mireles James, J. D. Computer assisted Fourier analysis in sequence spaces of varying regularity. (English) Zbl 1362.42007 SIAM J. Math. Anal. 49, No. 1, 530-561 (2017). MSC: 42A16 65N35 PDFBibTeX XMLCite \textit{J.-P. Lessard} and \textit{J. D. Mireles James}, SIAM J. Math. Anal. 49, No. 1, 530--561 (2017; Zbl 1362.42007) Full Text: DOI
Lessard, Jean-Philippe; Mireles James, J. D.; Ransford, Julian Automatic differentiation for Fourier series and the radii polynomial approach. (English) Zbl 1418.34094 Physica D 334, 174-186 (2016). MSC: 34C25 68W30 PDFBibTeX XMLCite \textit{J.-P. Lessard} et al., Physica D 334, 174--186 (2016; Zbl 1418.34094) Full Text: DOI
de la Llave, R.; Mireles James, J. D. Connecting orbits for compact infinite dimensional maps: computer assisted proofs of existence. (English) Zbl 1343.37078 SIAM J. Appl. Dyn. Syst. 15, No. 2, 1268-1323 (2016). MSC: 37L25 37M99 65P99 65G20 PDFBibTeX XMLCite \textit{R. de la Llave} and \textit{J. D. Mireles James}, SIAM J. Appl. Dyn. Syst. 15, No. 2, 1268--1323 (2016; Zbl 1343.37078) Full Text: DOI
Hungria, Allan; Lessard, Jean-Philippe; Mireles James, J. D. Rigorous numerics for analytic solutions of differential equations: the radii polynomial approach. (English) Zbl 1332.65114 Math. Comput. 85, No. 299, 1427-1459 (2016). MSC: 65L60 65G40 34C25 35K57 PDFBibTeX XMLCite \textit{A. Hungria} et al., Math. Comput. 85, No. 299, 1427--1459 (2016; Zbl 1332.65114) Full Text: DOI Link
Lessard, Jean-Philippe; Desvillettes, Laurent; Breden, Maxime Rigorous numerics for nonlinear operators with tridiagonal dominant linear part. (English) Zbl 1337.47114 Discrete Contin. Dyn. Syst. 35, No. 10, 4765-4789 (2015). MSC: 47N40 65J15 47A66 PDFBibTeX XMLCite \textit{J.-P. Lessard} et al., Discrete Contin. Dyn. Syst. 35, No. 10, 4765--4789 (2015; Zbl 1337.47114) Full Text: DOI arXiv
Alexander, Zachary; Bradley, Elizabeth; Meiss, James D.; Sanderson, Nicole F. Simplicial multivalued maps and the witness complex for dynamical analysis of time series. (English) Zbl 1320.37034 SIAM J. Appl. Dyn. Syst. 14, No. 3, 1278-1307 (2015). MSC: 37M10 65P20 55U10 37C70 PDFBibTeX XMLCite \textit{Z. Alexander} et al., SIAM J. Appl. Dyn. Syst. 14, No. 3, 1278--1307 (2015; Zbl 1320.37034) Full Text: DOI arXiv
Galias, Zbigniew Automatized search for complex symbolic dynamics with applications in the analysis of a simple memristor circuit. (English) Zbl 1300.37011 Int. J. Bifurcation Chaos Appl. Sci. Eng. 24, No. 7, Article ID 1450104, 11 p. (2014). MSC: 37B10 37B40 94C05 PDFBibTeX XMLCite \textit{Z. Galias}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 24, No. 7, Article ID 1450104, 11 p. (2014; Zbl 1300.37011) Full Text: DOI
O’Regan, Suzanne M.; Kelly, Thomas C.; Korobeinikov, Andrei; O’Callaghan, Michael J. A.; Pokrovskii, Alexei V.; Rachinskii, Dmitrii Chaos in a seasonally perturbed SIR model: avian influenza in a seabird colony as a paradigm. (English) Zbl 1286.37074 J. Math. Biol. 67, No. 2, 293-327 (2013). MSC: 37N25 37B55 37D45 92B05 92D40 PDFBibTeX XMLCite \textit{S. M. O'Regan} et al., J. Math. Biol. 67, No. 2, 293--327 (2013; Zbl 1286.37074) Full Text: DOI Link
Bush, Justin; Gameiro, Marcio; Harker, Shaun; Kokubu, Hiroshi; Mischaikow, Konstantin; Obayashi, Ippei; Pilarczyk, Paweł Combinatorial-topological framework for the analysis of global dynamics. (English) Zbl 1319.37004 Chaos 22, No. 4, 047508, 16 p. (2012). MSC: 37-04 37M20 37N30 37E25 PDFBibTeX XMLCite \textit{J. Bush} et al., Chaos 22, No. 4, 047508, 16 p. (2012; Zbl 1319.37004) Full Text: DOI Link
Arai, Zin; Kokubu, Hiroshi; Pilarczyk, Paweł Recent development in rigorous computational methods in dynamical systems. (English) Zbl 1184.65117 Japan J. Ind. Appl. Math. 26, No. 2-3, 393-417 (2009). MSC: 65P30 65C40 37C27 37C29 37M20 37G15 PDFBibTeX XMLCite \textit{Z. Arai} et al., Japan J. Ind. Appl. Math. 26, No. 2--3, 393--417 (2009; Zbl 1184.65117) Full Text: DOI Euclid
Mrozek, Marian; Pilarczyk, Paweł; Ẓelazna, Natalia Homology algorithm based on acyclic subspace. (English) Zbl 1142.15300 Comput. Math. Appl. 55, No. 11, 2395-2412 (2008). MSC: 15A04 65F30 PDFBibTeX XMLCite \textit{M. Mrozek} et al., Comput. Math. Appl. 55, No. 11, 2395--2412 (2008; Zbl 1142.15300) Full Text: DOI
Pilarczyk, Paweł; Stolot, Kinga Excision-preserving cubical approach to the algorithmic computation of the discrete Conley index. (English) Zbl 1149.37010 Topology Appl. 155, No. 10, 1149-1162 (2008). Reviewer: Roman Srzednicki (Kraków) MSC: 37B30 37M99 PDFBibTeX XMLCite \textit{P. Pilarczyk} and \textit{K. Stolot}, Topology Appl. 155, No. 10, 1149--1162 (2008; Zbl 1149.37010) Full Text: DOI
Galias, Zbigniew; Zgliczyński, Piotr Infinite dimensional Krawczyk operator for finding periodic orbits of discrete dynamical systems. (English) Zbl 1148.37041 Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 12, 4261-4272 (2007). MSC: 37M99 34C25 37C27 65G30 37N25 92D25 PDFBibTeX XMLCite \textit{Z. Galias} and \textit{P. Zgliczyński}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 12, 4261--4272 (2007; Zbl 1148.37041) Full Text: DOI
Hiraoka, Yasuaki; Ogawa, Toshiyuki Rigorous numerics for localized patterns to the quintic Swift-Hohenberg equation. (English) Zbl 1067.65146 Japan J. Ind. Appl. Math. 22, No. 1, 57-75 (2005). MSC: 65P30 37K50 37M20 PDFBibTeX XMLCite \textit{Y. Hiraoka} and \textit{T. Ogawa}, Japan J. Ind. Appl. Math. 22, No. 1, 57--75 (2005; Zbl 1067.65146) Full Text: DOI