Goh, Ryan; Kaper, Tasso J.; Scheel, Arnd; Vo, Theodore Fronts in the wake of a parameter ramp: slow passage through pitchfork and fold bifurcations. (English) Zbl 07741159 SIAM J. Appl. Dyn. Syst. 22, No. 3, 2312-2356 (2023). MSC: 34E15 34E13 35B25 35B36 PDFBibTeX XMLCite \textit{R. Goh} et al., SIAM J. Appl. Dyn. Syst. 22, No. 3, 2312--2356 (2023; Zbl 07741159) Full Text: DOI arXiv
Kaklamanos, Panagiotis; Popović, Nikola; Kristiansen, Kristian U. Geometric singular perturbation analysis of the multiple-timescale Hodgkin-Huxley equations. (English) Zbl 1522.34074 SIAM J. Appl. Dyn. Syst. 22, No. 3, 1552-1589 (2023). MSC: 34C60 92C20 34E15 34E13 34A26 34C20 34C23 34C26 PDFBibTeX XMLCite \textit{P. Kaklamanos} et al., SIAM J. Appl. Dyn. Syst. 22, No. 3, 1552--1589 (2023; Zbl 1522.34074) Full Text: DOI arXiv
Kristiansen, Kristian Uldall; Pedersen, Morten Gram Mixed-mode oscillations in coupled Fitzhugh-Nagumo oscillators: blow-up analysis of cusped singularities. (English) Zbl 1521.34058 SIAM J. Appl. Dyn. Syst. 22, No. 2, 1383-1422 (2023). MSC: 34C60 92C20 34E15 34A26 34C26 34C23 34C45 34C14 34C05 34E17 PDFBibTeX XMLCite \textit{K. U. Kristiansen} and \textit{M. G. Pedersen}, SIAM J. Appl. Dyn. Syst. 22, No. 2, 1383--1422 (2023; Zbl 1521.34058) Full Text: DOI arXiv
Ikeda, Hideo Existence and stability of standing spot solutions in a three-component FitzHugh-Nagumo system in \(R^2\). (English) Zbl 1523.35022 SIAM J. Appl. Dyn. Syst. 22, No. 2, 951-995 (2023). Reviewer: Paolo Musolino (Padova) MSC: 35B25 35B32 35B35 35K40 35K57 35K59 34D15 PDFBibTeX XMLCite \textit{H. Ikeda}, SIAM J. Appl. Dyn. Syst. 22, No. 2, 951--995 (2023; Zbl 1523.35022) Full Text: DOI
Cihak, Heather L.; Eissa, Tahra L.; Kilpatrick, Zachary P. Distinct excitatory and inhibitory bump wandering in a stochastic neural field. (English) Zbl 1504.35579 SIAM J. Appl. Dyn. Syst. 21, No. 4, 2579-2609 (2022). MSC: 35Q92 92C20 35B36 35B41 35B35 35B20 35B40 82C31 35R60 PDFBibTeX XMLCite \textit{H. L. Cihak} et al., SIAM J. Appl. Dyn. Syst. 21, No. 4, 2579--2609 (2022; Zbl 1504.35579) Full Text: DOI arXiv
Pnueli, Michal; Rom-Kedar, Vered Near tangent dynamics in a class of Hamiltonian impact systems. (English) Zbl 1510.37095 SIAM J. Appl. Dyn. Syst. 21, No. 3, 2000-2046 (2022). Reviewer: Diogo Pinheiro (New York) MSC: 37J40 37C83 70H08 70H09 70K43 PDFBibTeX XMLCite \textit{M. Pnueli} and \textit{V. Rom-Kedar}, SIAM J. Appl. Dyn. Syst. 21, No. 3, 2000--2046 (2022; Zbl 1510.37095) Full Text: DOI arXiv
Jelbart, Samuel; Pages, Nathan; Kirk, Vivien; Sneyd, James; Wechselberger, Martin Process-oriented geometric singular perturbation theory and calcium dynamics. (English) Zbl 1497.34060 SIAM J. Appl. Dyn. Syst. 21, No. 2, 982-1029 (2022). MSC: 34C15 34C26 34E15 92C37 34E13 93B30 PDFBibTeX XMLCite \textit{S. Jelbart} et al., SIAM J. Appl. Dyn. Syst. 21, No. 2, 982--1029 (2022; Zbl 1497.34060) Full Text: DOI arXiv
Feliu, Elisenda; Lax, Christian; Walcher, Sebastian; Wiuf, Carsten Quasi-steady-state and singular perturbation reduction for reaction networks with noninteracting species. (English) Zbl 1496.92029 SIAM J. Appl. Dyn. Syst. 21, No. 2, 782-816 (2022). Reviewer: Dieter Erle (Dortmund) MSC: 92C45 92C42 92D25 34E15 34C20 05C92 05C90 92E10 PDFBibTeX XMLCite \textit{E. Feliu} et al., SIAM J. Appl. Dyn. Syst. 21, No. 2, 782--816 (2022; Zbl 1496.92029) Full Text: DOI arXiv
Cheesman, Noah; Kristiansen, Kristian Uldall; Hogan, S. J. Regularization of isolated codimension-2 discontinuity sets. (English) Zbl 1494.34073 SIAM J. Appl. Dyn. Syst. 20, No. 4, 2630-2670 (2021). Reviewer: Dingheng Pi (Quanzhou) MSC: 34A36 34E15 74H35 70F40 PDFBibTeX XMLCite \textit{N. Cheesman} et al., SIAM J. Appl. Dyn. Syst. 20, No. 4, 2630--2670 (2021; Zbl 1494.34073) Full Text: DOI arXiv
Eilertsen, Justin; Tyczynska, Malgorzata Anna; Schnell, Santiago Hunting \(\varepsilon\): the origin and validity of quasi-steady-state reductions in enzyme kinetics. (English) Zbl 1481.92051 SIAM J. Appl. Dyn. Syst. 20, No. 4, 2450-2481 (2021). MSC: 92C45 34D15 PDFBibTeX XMLCite \textit{J. Eilertsen} et al., SIAM J. Appl. Dyn. Syst. 20, No. 4, 2450--2481 (2021; Zbl 1481.92051) Full Text: DOI arXiv
Creedon, Ryan; Deconinck, Bernard; Trichtchenko, Olga High-frequency instabilities of the Kawahara equation: a perturbative approach. (English) Zbl 1478.35072 SIAM J. Appl. Dyn. Syst. 20, No. 3, 1571-1595 (2021). MSC: 35C07 35B35 35G25 37K45 34L05 PDFBibTeX XMLCite \textit{R. Creedon} et al., SIAM J. Appl. Dyn. Syst. 20, No. 3, 1571--1595 (2021; Zbl 1478.35072) Full Text: DOI arXiv
Gimeno, Joan; Yang, Jiaqi; de la Llave, Rafael Numerical computation of periodic orbits and isochrons for state-dependent delay perturbation of an ODE in the plane. (English) Zbl 1487.37094 SIAM J. Appl. Dyn. Syst. 20, No. 3, 1514-1543 (2021). Reviewer: Fernando Casas (Castellon) MSC: 37M05 37M21 37C27 34C07 34C25 PDFBibTeX XMLCite \textit{J. Gimeno} et al., SIAM J. Appl. Dyn. Syst. 20, No. 3, 1514--1543 (2021; Zbl 1487.37094) Full Text: DOI arXiv
Bauer, Adam; Carter, Paul Existence of transonic solutions in the stellar wind problem with viscosity and heat conduction. (English) Zbl 1464.76048 SIAM J. Appl. Dyn. Syst. 20, No. 1, 262-298 (2021). MSC: 76H05 76M45 35Q35 85A30 80A19 PDFBibTeX XMLCite \textit{A. Bauer} and \textit{P. Carter}, SIAM J. Appl. Dyn. Syst. 20, No. 1, 262--298 (2021; Zbl 1464.76048) Full Text: DOI
Huang, Jianfeng; Torregrosa, Joan; Villadelprat, Jordi On the number of limit cycles in generalized Abel equations. (English) Zbl 1472.34065 SIAM J. Appl. Dyn. Syst. 19, No. 4, 2343-2370 (2020). Reviewer: Klaus R. Schneider (Berlin) MSC: 34C07 34C05 37C60 PDFBibTeX XMLCite \textit{J. Huang} et al., SIAM J. Appl. Dyn. Syst. 19, No. 4, 2343--2370 (2020; Zbl 1472.34065) Full Text: DOI
Kristiansen, Kristian U. On the pitchfork bifurcation of the folded node and other unbounded time-reversible connection problems in \(\mathbb{R}^3\). (English) Zbl 1470.37074 SIAM J. Appl. Dyn. Syst. 19, No. 3, 2059-2102 (2020). MSC: 37G25 37C27 37C29 34A26 34E15 34E17 PDFBibTeX XMLCite \textit{K. U. Kristiansen}, SIAM J. Appl. Dyn. Syst. 19, No. 3, 2059--2102 (2020; Zbl 1470.37074) Full Text: DOI arXiv
Sanford, Nathan L.; Donovan, Graham M.; Kath, William L. Slip rates and slip modes in an actively mode-locked laser. (English) Zbl 1447.35303 SIAM J. Appl. Dyn. Syst. 19, No. 2, 1472-1495 (2020). Reviewer: Boris A. Malomed (Tel Aviv) MSC: 35Q56 35Q51 35Q60 78A60 65C05 65C20 PDFBibTeX XMLCite \textit{N. L. Sanford} et al., SIAM J. Appl. Dyn. Syst. 19, No. 2, 1472--1495 (2020; Zbl 1447.35303) Full Text: DOI
Prasadan, Arvind; Nadakuditi, Raj Rao Time series source separation using dynamic mode decomposition. (English) Zbl 1445.37057 SIAM J. Appl. Dyn. Syst. 19, No. 2, 1160-1199 (2020). MSC: 37M10 62M10 47A55 47A75 60G35 37N30 PDFBibTeX XMLCite \textit{A. Prasadan} and \textit{R. R. Nadakuditi}, SIAM J. Appl. Dyn. Syst. 19, No. 2, 1160--1199 (2020; Zbl 1445.37057) Full Text: DOI arXiv
Lizarraga, Ian; Wechselberger, Martin Computational singular perturbation method for nonstandard slow-fast systems. (English) Zbl 1457.37102 SIAM J. Appl. Dyn. Syst. 19, No. 2, 994-1028 (2020). Reviewer: Oleg Anashkin (Simferopol) MSC: 37M21 34D10 34D15 70K70 PDFBibTeX XMLCite \textit{I. Lizarraga} and \textit{M. Wechselberger}, SIAM J. Appl. Dyn. Syst. 19, No. 2, 994--1028 (2020; Zbl 1457.37102) Full Text: DOI arXiv
Bosschaert, Maikel M.; Janssens, Sebastiaan G.; Kuznetsov, Yu. A. Switching to nonhyperbolic cycles from codimension two bifurcations of equilibria of delay differential equations. (English) Zbl 07175469 SIAM J. Appl. Dyn. Syst. 19, No. 1, 252-303 (2020). Reviewer: Jian Peng (Xiangtan) MSC: 34K18 34K19 34K60 37L10 37M20 PDFBibTeX XMLCite \textit{M. M. Bosschaert} et al., SIAM J. Appl. Dyn. Syst. 19, No. 1, 252--303 (2020; Zbl 07175469) 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
de la Llave, Rafael; Kogelbauer, Florian Global persistence of Lyapunov subcenter manifolds as spectral submanifolds under dissipative perturbations. (English) Zbl 1473.70033 SIAM J. Appl. Dyn. Syst. 18, No. 4, 2099-2142 (2019). MSC: 70H09 70H12 34D15 34C45 PDFBibTeX XMLCite \textit{R. de la Llave} and \textit{F. Kogelbauer}, SIAM J. Appl. Dyn. Syst. 18, No. 4, 2099--2142 (2019; Zbl 1473.70033) Full Text: DOI arXiv
Kaklamanos, Panagiotis; Kristiansen, Kristian U. Regularization and geometry of piecewise smooth systems with intersecting discontinuity sets. (English) Zbl 1431.37046 SIAM J. Appl. Dyn. Syst. 18, No. 3, 1225-1264 (2019). Reviewer: Robert Vrabel (Trnava) MSC: 37G10 34E15 37G25 37M20 PDFBibTeX XMLCite \textit{P. Kaklamanos} and \textit{K. U. Kristiansen}, SIAM J. Appl. Dyn. Syst. 18, No. 3, 1225--1264 (2019; Zbl 1431.37046) Full Text: DOI arXiv
Cardin, Pedro Toniol; Teixeira, Marco Antonio Corrigendum to: “Fenichel theory for multiple time scale singular perturbation problems”. (English) Zbl 1471.34113 SIAM J. Appl. Dyn. Syst. 18, No. 2, 1223 (2019). MSC: 34E15 34C20 34C45 PDFBibTeX XMLCite \textit{P. T. Cardin} and \textit{M. A. Teixeira}, SIAM J. Appl. Dyn. Syst. 18, No. 2, 1223 (2019; Zbl 1471.34113) Full Text: DOI
Ziepke, Alexander; Martens, Steffen; Engel, Harald Control of nonlinear wave solutions to neural field equations. (English) Zbl 1435.45005 SIAM J. Appl. Dyn. Syst. 18, No. 2, 1015-1036 (2019). MSC: 45K05 45Q05 92C20 93C95 PDFBibTeX XMLCite \textit{A. Ziepke} et al., SIAM J. Appl. Dyn. Syst. 18, No. 2, 1015--1036 (2019; Zbl 1435.45005) Full Text: DOI arXiv
Iuorio, Annalisa; Popović, Nikola; Szmolyan, Peter Singular perturbation analysis of a regularized MEMS model. (English) Zbl 1458.34103 SIAM J. Appl. Dyn. Syst. 18, No. 2, 661-708 (2019). Reviewer: Vasile Dragan (Bucureşti) MSC: 34E15 34B16 34C23 34E05 35K67 35B25 PDFBibTeX XMLCite \textit{A. Iuorio} et al., SIAM J. Appl. Dyn. Syst. 18, No. 2, 661--708 (2019; Zbl 1458.34103) Full Text: DOI arXiv
Pnueli, Michal; Rom-Kedar, Vered On near integrability of some impact systems. (English) Zbl 1405.37067 SIAM J. Appl. Dyn. Syst. 17, No. 4, 2707-2732 (2018). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 37J40 37J25 70H07 70H08 70H09 74M20 PDFBibTeX XMLCite \textit{M. Pnueli} and \textit{V. Rom-Kedar}, SIAM J. Appl. Dyn. Syst. 17, No. 4, 2707--2732 (2018; Zbl 1405.37067) Full Text: DOI arXiv
Reverdy, Paul; Koditschek, Daniel E. A dynamical system for prioritizing and coordinating motivations. (English) Zbl 1393.37104 SIAM J. Appl. Dyn. Syst. 17, No. 2, 1683-1715 (2018). MSC: 37N35 37G25 37D10 62C05 PDFBibTeX XMLCite \textit{P. Reverdy} and \textit{D. E. Koditschek}, SIAM J. Appl. Dyn. Syst. 17, No. 2, 1683--1715 (2018; Zbl 1393.37104) Full Text: DOI arXiv
Ha, Seung-Yeal; Lee, Jaeseung; Li, Zhuchun; Park, Jinyeong Emergent dynamics of Kuramoto oscillators with adaptive couplings: conservation law and fast learning. (English) Zbl 1401.70030 SIAM J. Appl. Dyn. Syst. 17, No. 2, 1560-1588 (2018). MSC: 70K20 34C15 92B25 PDFBibTeX XMLCite \textit{S.-Y. Ha} et al., SIAM J. Appl. Dyn. Syst. 17, No. 2, 1560--1588 (2018; Zbl 1401.70030) Full Text: DOI
Wang, Cheng; Zhang, Xiang Stability loss delay and smoothness of the return map in slow-fast systems. (English) Zbl 1396.34042 SIAM J. Appl. Dyn. Syst. 17, No. 1, 788-822 (2018). Reviewer: Vasile Dragan (Bucureşti) MSC: 34E15 34E20 34D05 34C20 34C05 PDFBibTeX XMLCite \textit{C. Wang} and \textit{X. Zhang}, SIAM J. Appl. Dyn. Syst. 17, No. 1, 788--822 (2018; Zbl 1396.34042) Full Text: DOI
Cornwell, Paul; Jones, Christopher K. R. T. On the existence and stability of fast traveling waves in a doubly diffusive FitzHugh-Nagumo system. (English) Zbl 1406.35041 SIAM J. Appl. Dyn. Syst. 17, No. 1, 754-787 (2018). MSC: 35B35 35C07 35B25 35P15 35K57 37J05 PDFBibTeX XMLCite \textit{P. Cornwell} and \textit{C. K. R. T. Jones}, SIAM J. Appl. Dyn. Syst. 17, No. 1, 754--787 (2018; Zbl 1406.35041) Full Text: DOI arXiv
Farjami, Saeed; Kirk, Vivien; Osinga, Hinke M. Computing the stable manifold of a saddle slow manifold. (English) Zbl 1403.37036 SIAM J. Appl. Dyn. Syst. 17, No. 1, 350-379 (2018). Reviewer: Josef Diblík (Brno) MSC: 37D10 37M20 34D15 34E15 37C10 65L10 34D35 34C45 65P40 70K70 PDFBibTeX XMLCite \textit{S. Farjami} et al., SIAM J. Appl. Dyn. Syst. 17, No. 1, 350--379 (2018; Zbl 1403.37036) Full Text: DOI
Carter, Paul; Sandstede, Björn Unpeeling a homoclinic banana in the FitzHugh-Nagumo system. (English) Zbl 1407.35015 SIAM J. Appl. Dyn. Syst. 17, No. 1, 236-349 (2018). MSC: 35B25 35C07 34E15 34E17 35K57 PDFBibTeX XMLCite \textit{P. Carter} and \textit{B. Sandstede}, SIAM J. Appl. Dyn. Syst. 17, No. 1, 236--349 (2018; Zbl 1407.35015) Full Text: DOI
Poll, Daniel B.; Kilpatrick, Zachary P. Velocity integration in a multilayer neural field model of spatial working memory. (English) Zbl 1417.92010 SIAM J. Appl. Dyn. Syst. 16, No. 3, 1197-1234 (2017). MSC: 92B20 60H10 34D10 PDFBibTeX XMLCite \textit{D. B. Poll} and \textit{Z. P. Kilpatrick}, SIAM J. Appl. Dyn. Syst. 16, No. 3, 1197--1234 (2017; Zbl 1417.92010) Full Text: DOI arXiv
Mitry, John; Wechselberger, Martin Folded saddles and faux canards. (English) Zbl 1418.34117 SIAM J. Appl. Dyn. Syst. 16, No. 1, 546-596 (2017). MSC: 34E17 34C23 34C45 37D10 37G25 65L10 65L11 PDFBibTeX XMLCite \textit{J. Mitry} and \textit{M. Wechselberger}, SIAM J. Appl. Dyn. Syst. 16, No. 1, 546--596 (2017; Zbl 1418.34117) Full Text: DOI
Holzer, Matt; Popović, Nikola Wavetrain solutions of a reaction-diffusion-advection model of mussel-algae interaction. (English) Zbl 1434.35256 SIAM J. Appl. Dyn. Syst. 16, No. 1, 431-478 (2017). MSC: 35Q92 35B36 35C07 35K57 35M30 PDFBibTeX XMLCite \textit{M. Holzer} and \textit{N. Popović}, SIAM J. Appl. Dyn. Syst. 16, No. 1, 431--478 (2017; Zbl 1434.35256) Full Text: DOI
Lee, Min-Gi; Tzavaras, Athanasios Existence of localizing solutions in plasticity via geometric singular perturbation theory. (English) Zbl 1434.35221 SIAM J. Appl. Dyn. Syst. 16, No. 1, 337-360 (2017). MSC: 35Q74 34C37 34C45 35M31 37C29 74C20 PDFBibTeX XMLCite \textit{M.-G. Lee} and \textit{A. Tzavaras}, SIAM J. Appl. Dyn. Syst. 16, No. 1, 337--360 (2017; Zbl 1434.35221) Full Text: DOI arXiv
Franci, Alessio; Sepulchre, Rodolphe A three-scale model of spatio-temporal bursting. (English) Zbl 1360.37182 SIAM J. Appl. Dyn. Syst. 15, No. 4, 2143-2175 (2016). MSC: 37N25 34E13 35K57 35B36 35K40 PDFBibTeX XMLCite \textit{A. Franci} and \textit{R. Sepulchre}, SIAM J. Appl. Dyn. Syst. 15, No. 4, 2143--2175 (2016; Zbl 1360.37182) Full Text: DOI arXiv
McQuighan, Kelly; Wayne, C. Eugene An explanation of metastability in the viscous Burgers equation with periodic boundary conditions via a spectral analysis. (English) Zbl 1361.35081 SIAM J. Appl. Dyn. Syst. 15, No. 4, 1916-1961 (2016). MSC: 35K55 34B16 34B24 34E15 35B40 35K67 PDFBibTeX XMLCite \textit{K. McQuighan} and \textit{C. E. Wayne}, SIAM J. Appl. Dyn. Syst. 15, No. 4, 1916--1961 (2016; Zbl 1361.35081) Full Text: DOI arXiv
Al-Hdaibat, B.; Govaerts, W.; Kuznetsov, Yu. A.; Meijer, H. G. E. Initialization of homoclinic solutions near Bogdanov-Takens points: Lindstedt-Poincaré compared with regular perturbation method. (English) Zbl 1343.34104 SIAM J. Appl. Dyn. Syst. 15, No. 2, 952-980 (2016). MSC: 34C37 34C23 65P30 34C20 34E10 37G20 37M20 PDFBibTeX XMLCite \textit{B. Al-Hdaibat} et al., SIAM J. Appl. Dyn. Syst. 15, No. 2, 952--980 (2016; Zbl 1343.34104) Full Text: DOI
Roberts, Kerry-Lyn; Rubin, Jonathan E.; Wechselberger, Martin Averaging, folded singularities, and torus canards: explaining transitions between bursting and spiking in a coupled neuron model. (English) Zbl 1360.37183 SIAM J. Appl. Dyn. Syst. 14, No. 4, 1808-1844 (2015). MSC: 37N25 34E17 92B25 37M05 37G35 PDFBibTeX XMLCite \textit{K.-L. Roberts} et al., SIAM J. Appl. Dyn. Syst. 14, No. 4, 1808--1844 (2015; Zbl 1360.37183) Full Text: DOI
Kristiansen, K. Uldall; Hogan, S. J. Regularizations of two-fold bifurcations in planar piecewise smooth systems using blowup. (English) Zbl 1353.37100 SIAM J. Appl. Dyn. Syst. 14, No. 4, 1731-1786 (2015). MSC: 37G10 34E15 34A36 34C23 34E17 PDFBibTeX XMLCite \textit{K. U. Kristiansen} and \textit{S. J. Hogan}, SIAM J. Appl. Dyn. Syst. 14, No. 4, 1731--1786 (2015; Zbl 1353.37100) Full Text: DOI arXiv
Nan, Pingyu; Wang, Yangyang; Kirk, Vivien; Rubin, Jonathan E. Understanding and distinguishing three-time-scale oscillations: case study in a coupled Morris-Lecar system. (English) Zbl 1329.34094 SIAM J. Appl. Dyn. Syst. 14, No. 3, 1518-1557 (2015). MSC: 34C60 34C15 34C26 34E15 92C20 34D15 PDFBibTeX XMLCite \textit{P. Nan} et al., SIAM J. Appl. Dyn. Syst. 14, No. 3, 1518--1557 (2015; Zbl 1329.34094) Full Text: DOI
Ghazaryan, Anna; Manukian, Vahagn Coherent structures in a population model for mussel-algae interaction. (English) Zbl 1314.35196 SIAM J. Appl. Dyn. Syst. 14, No. 2, 893-913 (2015). MSC: 35Q92 35B25 35B32 35K57 35B36 92D25 PDFBibTeX XMLCite \textit{A. Ghazaryan} and \textit{V. Manukian}, SIAM J. Appl. Dyn. Syst. 14, No. 2, 893--913 (2015; Zbl 1314.35196) Full Text: DOI Link
Kristiansen, K. Uldall; Hogan, S. J. On the use of blowup to study regularizations of singularities of piecewise smooth dynamical systems in \(\mathbb{R}^3\). (English) Zbl 1370.37100 SIAM J. Appl. Dyn. Syst. 14, No. 1, 382-422 (2015). MSC: 37G10 34E15 34A36 37M20 PDFBibTeX XMLCite \textit{K. U. Kristiansen} and \textit{S. J. Hogan}, SIAM J. Appl. Dyn. Syst. 14, No. 1, 382--422 (2015; Zbl 1370.37100) Full Text: DOI arXiv
Kloc, M.; Rom-Kedar, V. Smooth Hamiltonian systems with soft impacts. (English) Zbl 1308.70028 SIAM J. Appl. Dyn. Syst. 13, No. 3, 1033-1059 (2014). MSC: 70H07 70H08 70H09 70H12 70H14 37J45 70F35 80A50 PDFBibTeX XMLCite \textit{M. Kloc} and \textit{V. Rom-Kedar}, SIAM J. Appl. Dyn. Syst. 13, No. 3, 1033--1059 (2014; Zbl 1308.70028) Full Text: DOI arXiv
Kristiansen, K. Uldall; Brøns, M.; Starke, J. An iterative method for the approximation of fibers in slow-fast systems. (English) Zbl 1301.34076 SIAM J. Appl. Dyn. Syst. 13, No. 2, 861-900 (2014). MSC: 34E15 34E13 37M99 34C45 PDFBibTeX XMLCite \textit{K. U. Kristiansen} et al., SIAM J. Appl. Dyn. Syst. 13, No. 2, 861--900 (2014; Zbl 1301.34076) Full Text: DOI arXiv
Faye, Grégory Existence and stability of traveling pulses in a neural field equation with synaptic depression. (English) Zbl 1282.34061 SIAM J. Appl. Dyn. Syst. 12, No. 4, 2032-2067 (2013). MSC: 34E15 34D23 35Q92 35C07 92B20 PDFBibTeX XMLCite \textit{G. Faye}, SIAM J. Appl. Dyn. Syst. 12, No. 4, 2032--2067 (2013; Zbl 1282.34061) Full Text: DOI Link
Neishtadt, Anatoly; Su, Tan On asymptotic description of passage through a resonance in quasilinear Hamiltonian systems. (English) Zbl 1285.34054 SIAM J. Appl. Dyn. Syst. 12, No. 3, 1436-1473 (2013). MSC: 34E10 70H11 37J40 PDFBibTeX XMLCite \textit{A. Neishtadt} and \textit{T. Su}, SIAM J. Appl. Dyn. Syst. 12, No. 3, 1436--1473 (2013; Zbl 1285.34054) Full Text: DOI arXiv
Bressloff, Paul C.; Newby, Jay M. Metastability in a stochastic neural network modeled as a velocity jump Markov process. (English) Zbl 1278.92005 SIAM J. Appl. Dyn. Syst. 12, No. 3, 1394-1435 (2013). MSC: 92C20 92B20 60J75 PDFBibTeX XMLCite \textit{P. C. Bressloff} and \textit{J. M. Newby}, SIAM J. Appl. Dyn. Syst. 12, No. 3, 1394--1435 (2013; Zbl 1278.92005) Full Text: DOI arXiv
Vo, Theodore; Bertram, Richard; Wechselberger, Martin Multiple geometric viewpoints of mixed mode dynamics associated with pseudo-plateau bursting. (English) Zbl 1295.37022 SIAM J. Appl. Dyn. Syst. 12, No. 2, 789-830 (2013). Reviewer: Paul Georgescu (Iaşi) MSC: 37N25 34E17 92B25 37M05 37G35 PDFBibTeX XMLCite \textit{T. Vo} et al., SIAM J. Appl. Dyn. Syst. 12, No. 2, 789--830 (2013; Zbl 1295.37022) Full Text: DOI
Veerman, Frits; Doelman, Arjen Pulses in a Gierer-Meinhardt equation with a slow nonlinearity. (English) Zbl 1282.35049 SIAM J. Appl. Dyn. Syst. 12, No. 1, 28-60 (2013). MSC: 35B36 35K57 35B25 35B35 35K45 PDFBibTeX XMLCite \textit{F. Veerman} and \textit{A. Doelman}, SIAM J. Appl. Dyn. Syst. 12, No. 1, 28--60 (2013; Zbl 1282.35049) Full Text: DOI Link
McCarthy, Michelle M.; Kopell, Nancy The effect of propofol anesthesia on rebound spiking. (English) Zbl 1263.37085 SIAM J. Appl. Dyn. Syst. 11, No. 4, 1674-1697 (2012). MSC: 37N25 92C20 92C40 PDFBibTeX XMLCite \textit{M. M. McCarthy} and \textit{N. Kopell}, SIAM J. Appl. Dyn. Syst. 11, No. 4, 1674--1697 (2012; Zbl 1263.37085) Full Text: DOI
Krupa, Martin; Vidal, Alexandre; Desroches, Mathieu; Clément, Frédérique Mixed-mode oscillations in a multiple time scale phantom bursting system. (English) Zbl 1260.34091 SIAM J. Appl. Dyn. Syst. 11, No. 4, 1458-1498 (2012). MSC: 34C60 34C15 34C23 34C26 34D15 34E13 34E15 34E17 70K70 92B05 PDFBibTeX XMLCite \textit{M. Krupa} et al., SIAM J. Appl. Dyn. Syst. 11, No. 4, 1458--1498 (2012; Zbl 1260.34091) Full Text: DOI arXiv
Kosiuk, Ilona; Szmolyan, Peter Scaling in singular perturbation problems: blowing up a relaxation oscillator. (English) Zbl 1243.34066 SIAM J. Appl. Dyn. Syst. 10, No. 4, 1307-1343 (2011). MSC: 34C60 34C26 34E15 92C40 34A26 PDFBibTeX XMLCite \textit{I. Kosiuk} and \textit{P. Szmolyan}, SIAM J. Appl. Dyn. Syst. 10, No. 4, 1307--1343 (2011; Zbl 1243.34066) Full Text: DOI
Hupkes, Hermen Jan; Sandstede, Björn Traveling pulse solutions for the discrete FitzHugh-Nagumo system. (English) Zbl 1211.34007 SIAM J. Appl. Dyn. Syst. 9, No. 3, 827-882 (2010). Reviewer: Zhi-Cheng Wang (Lanzhou) MSC: 34A33 34D35 34E20 34B15 PDFBibTeX XMLCite \textit{H. J. Hupkes} and \textit{B. Sandstede}, SIAM J. Appl. Dyn. Syst. 9, No. 3, 827--882 (2010; Zbl 1211.34007) Full Text: DOI
Guckenheimer, John; Kuehn, Christian Homoclinic orbits of the FitzHugh-Nagumo equation: bifurcations in the full system. (English) Zbl 1210.34060 SIAM J. Appl. Dyn. Syst. 9, No. 1, 138-153 (2010). Reviewer: E. V. Shchetinina (Samara) MSC: 34C37 34E13 34E15 37G20 34C26 37D45 34C23 34C45 PDFBibTeX XMLCite \textit{J. Guckenheimer} and \textit{C. Kuehn}, SIAM J. Appl. Dyn. Syst. 9, No. 1, 138--153 (2010; Zbl 1210.34060) Full Text: DOI arXiv
Chiba, Hayato Extension and unification of singular perturbation methods for ODEs based on the renormalization group method. (English) Zbl 1179.34035 SIAM J. Appl. Dyn. Syst. 8, No. 3, 1066-1115 (2009). Reviewer: Vasile Dragan (Bucureşti) MSC: 34C20 34C29 34E15 34C14 34C45 PDFBibTeX XMLCite \textit{H. Chiba}, SIAM J. Appl. Dyn. Syst. 8, No. 3, 1066--1115 (2009; Zbl 1179.34035) Full Text: DOI arXiv
Schecter, Stephen; Szmolyan, Peter Persistence of rarefactions under Dafermos regularization: blow-up and an exchange lemma for gain-of-stability turning points. (English) Zbl 1178.35252 SIAM J. Appl. Dyn. Syst. 8, No. 3, 822-853 (2009). Reviewer: Evgeniy Panov (Novgorod) MSC: 35L65 34E15 35B44 PDFBibTeX XMLCite \textit{S. Schecter} and \textit{P. Szmolyan}, SIAM J. Appl. Dyn. Syst. 8, No. 3, 822--853 (2009; Zbl 1178.35252) Full Text: DOI Link
Beck, Margaret; Jones, Christopher K. R. T.; Schaeffer, David; Wechselberger, Martin Electrical waves in a one-dimensional model of cardiac tissue. (English) Zbl 1167.34364 SIAM J. Appl. Dyn. Syst. 7, No. 4, 1558-1581 (2008). MSC: 34E15 35K57 37L15 92C30 35B35 34B40 34C37 35P15 PDFBibTeX XMLCite \textit{M. Beck} et al., SIAM J. Appl. Dyn. Syst. 7, No. 4, 1558--1581 (2008; Zbl 1167.34364) Full Text: DOI Link
Desroches, M.; Krauskopf, B.; Osinga, H. M. The geometry of slow manifolds near a folded node. (English) Zbl 1167.34365 SIAM J. Appl. Dyn. Syst. 7, No. 4, 1131-1162 (2008). MSC: 34E15 34C30 65L10 34C26 34C23 PDFBibTeX XMLCite \textit{M. Desroches} et al., SIAM J. Appl. Dyn. Syst. 7, No. 4, 1131--1162 (2008; Zbl 1167.34365) Full Text: DOI Link
Chiba, Hayato \(C^1\) approximation of vector fields based on the renormalization group method. (English) Zbl 1159.37014 SIAM J. Appl. Dyn. Syst. 7, No. 3, 895-932 (2008). MSC: 37F25 34C15 34C20 37D10 37G10 PDFBibTeX XMLCite \textit{H. Chiba}, SIAM J. Appl. Dyn. Syst. 7, No. 3, 895--932 (2008; Zbl 1159.37014) Full Text: DOI
Xu, Jian; Chung, Kwok-Wai; Chan, Chuen-Lit An efficient method for studying weak resonant double Hopf bifurcation in nonlinear systems with delayed feedbacks. (English) Zbl 1210.34086 SIAM J. Appl. Dyn. Syst. 6, No. 1, 29-60 (2007). MSC: 34K06 37H20 70K30 74G10 93B52 PDFBibTeX XMLCite \textit{J. Xu} et al., SIAM J. Appl. Dyn. Syst. 6, No. 1, 29--60 (2007; Zbl 1210.34086) Full Text: DOI Link
Goodman, Roy H.; Haberman, Richard Kink-antikink collisions in the \(\phi^4\) equation: the \(n\)-bounce resonance and the separatrix map. (English) Zbl 1145.74370 SIAM J. Appl. Dyn. Syst. 4, No. 4, 1195-1228 (2005). MSC: 74J30 35Q51 35Q72 37D05 70K44 PDFBibTeX XMLCite \textit{R. H. Goodman} and \textit{R. Haberman}, SIAM J. Appl. Dyn. Syst. 4, No. 4, 1195--1228 (2005; Zbl 1145.74370) Full Text: DOI
Porter, Mason A.; Kevrekidis, P. G. Bose-Einstein condensates in superlattices. (English) Zbl 1145.82309 SIAM J. Appl. Dyn. Syst. 4, No. 4, 783-807 (2005). MSC: 82B10 37J40 81V45 PDFBibTeX XMLCite \textit{M. A. Porter} and \textit{P. G. Kevrekidis}, SIAM J. Appl. Dyn. Syst. 4, No. 4, 783--807 (2005; Zbl 1145.82309) Full Text: DOI arXiv Link
Wechselberger, Martin Existence and bifurcation of canards in \(\mathbb R^3\) in the case of a folded node. (English) Zbl 1090.34047 SIAM J. Appl. Dyn. Syst. 4, No. 1, 101-139 (2005). MSC: 34E15 34C15 92C20 34C23 34C45 PDFBibTeX XMLCite \textit{M. Wechselberger}, SIAM J. Appl. Dyn. Syst. 4, No. 1, 101--139 (2005; Zbl 1090.34047) Full Text: DOI
Doelman, Arjen; Kaper, Tasso J. Semistrong pulse interactions in a class of coupled reaction-diffusion equations. (English) Zbl 1088.35517 SIAM J. Appl. Dyn. Syst. 2, No. 1, 53-96 (2003). MSC: 35K57 35K45 35B25 35B32 35B40 34C30 34C37 92E20 PDFBibTeX XMLCite \textit{A. Doelman} and \textit{T. J. Kaper}, SIAM J. Appl. Dyn. Syst. 2, No. 1, 53--96 (2003; Zbl 1088.35517) Full Text: DOI
Patrick, George W. Stability by KAM confinement of certain wild, nongeneric relative equilibria of underwater vehicles with coincident centers of mass and Buoyancy. (English) Zbl 1088.37513 SIAM J. Appl. Dyn. Syst. 2, No. 1, 36-52 (2003). MSC: 37J25 70H14 37J40 70H09 37J15 70H33 PDFBibTeX XMLCite \textit{G. W. Patrick}, SIAM J. Appl. Dyn. Syst. 2, No. 1, 36--52 (2003; Zbl 1088.37513) Full Text: DOI arXiv