Cihak, Heather L.; Kilpatrick, Zachary P. Multiscale motion and deformation of bumps in stochastic neural fields with dynamic connectivity. (English) Zbl 07813973 Multiscale Model. Simul. 22, No. 1, 178-203 (2024). MSC: 35Q92 35B36 60G07 PDFBibTeX XMLCite \textit{H. L. Cihak} and \textit{Z. P. Kilpatrick}, Multiscale Model. Simul. 22, No. 1, 178--203 (2024; Zbl 07813973) Full Text: DOI arXiv
Mohan, Manil T. Large deviations for the two-time-scale stochastic convective Brinkman-Forchheimer equations. (English) Zbl 07757715 J. Differ. Equations 376, 469-537 (2023). MSC: 60H15 60F10 76Dxx 35R60 35Q30 PDFBibTeX XMLCite \textit{M. T. Mohan}, J. Differ. Equations 376, 469--537 (2023; Zbl 07757715) Full Text: DOI arXiv
Liu, Wei; Röckner, Michael; Sun, Xiaobin; Xie, Yingchao Strong averaging principle for slow-fast stochastic partial differential equations with locally monotone coefficients. (English) Zbl 1516.60039 Appl. Math. Optim. 87, No. 3, Paper No. 39, 31 p. (2023). Reviewer: Martin Ondreját (Praha) MSC: 60H15 70K70 35Q35 PDFBibTeX XMLCite \textit{W. Liu} et al., Appl. Math. Optim. 87, No. 3, Paper No. 39, 31 p. (2023; Zbl 1516.60039) Full Text: DOI arXiv
Avitabile, Daniele; Davis, Joshua L.; Wedgwood, Kyle Bump attractors and waves in networks of leaky integrate-and-fire neurons. (English) Zbl 1515.37103 SIAM Rev. 65, No. 1, 147-182 (2023). Reviewer: Haydar Akca (Abu Dhabi) MSC: 37N25 37M05 49J52 35B36 92C15 92B20 PDFBibTeX XMLCite \textit{D. Avitabile} et al., SIAM Rev. 65, No. 1, 147--182 (2023; Zbl 1515.37103) Full Text: DOI arXiv
Zhao, Na; Song, Jian; Liu, Shenquan Multi-timescale analysis of midbrain dopamine neuronal firing activities. (English) Zbl 1504.92014 J. Theor. Biol. 556, Article ID 111310, 14 p. (2023). MSC: 92B20 35B32 PDFBibTeX XMLCite \textit{N. Zhao} et al., J. Theor. Biol. 556, Article ID 111310, 14 p. (2023; Zbl 1504.92014) Full Text: DOI
Hong, Wei; Li, Miaomiao; Li, Shihu; Liu, Wei Large deviations and averaging for stochastic tamed 3D Navier-Stokes equations with fast oscillations. (English) Zbl 1498.60108 Appl. Math. Optim. 86, No. 2, Paper No. 15, 54 p. (2022). Reviewer: Martin Ondreját (Praha) MSC: 60F10 35Q30 60H15 35R60 PDFBibTeX XMLCite \textit{W. Hong} et al., Appl. Math. Optim. 86, No. 2, Paper No. 15, 54 p. (2022; Zbl 1498.60108) Full Text: DOI
Vainchtein, Anna Solitary waves in FPU-type lattices. (English) Zbl 07529695 Physica D 434, Article ID 133252, 22 p. (2022). MSC: 82-XX 35-XX PDFBibTeX XMLCite \textit{A. Vainchtein}, Physica D 434, Article ID 133252, 22 p. (2022; Zbl 07529695) Full Text: DOI
Zhang, Jianjun; Felix, Diego; Medeiros, Everaldo On a sharp weighted Sobolev inequality on the upper half-space and its applications. (English) Zbl 1489.35133 SN Partial Differ. Equ. Appl. 3, No. 2, Paper No. 30, 17 p. (2022). MSC: 35J87 47J20 35J62 35J25 35A01 46E35 PDFBibTeX XMLCite \textit{J. Zhang} et al., SN Partial Differ. Equ. Appl. 3, No. 2, Paper No. 30, 17 p. (2022; Zbl 1489.35133) Full Text: DOI
Hong, Wei; Li, Shihu; Liu, Wei Strong convergence rates in averaging principle for slow-fast McKean-Vlasov SPDEs. (English) Zbl 1487.60123 J. Differ. Equations 316, 94-135 (2022). Reviewer: David Prömel (Mannheim) MSC: 60H15 35R60 70K70 PDFBibTeX XMLCite \textit{W. Hong} et al., J. Differ. Equations 316, 94--135 (2022; Zbl 1487.60123) Full Text: DOI arXiv
Carvalho, Jonison L.; Furtado, Marcelo F.; Medeiros, Everaldo S. A sharp Hardy-Sobolev inequality with boundary term and applications. (English) Zbl 1481.35203 NoDEA, Nonlinear Differ. Equ. Appl. 29, No. 1, Paper No. 5, 20 p. (2022). MSC: 35J62 35J66 35A01 PDFBibTeX XMLCite \textit{J. L. Carvalho} et al., NoDEA, Nonlinear Differ. Equ. Appl. 29, No. 1, Paper No. 5, 20 p. (2022; Zbl 1481.35203) Full Text: DOI
Cheng, Jiahui; Tang, Sui Estimate the spectrum of affine dynamical systems from partial observations of a single trajectory data. (English) Zbl 1479.94087 Inverse Probl. 38, No. 1, Article ID 015004, 42 p. (2022). MSC: 94A20 94A12 42C15 93B30 46B15 35R30 PDFBibTeX XMLCite \textit{J. Cheng} and \textit{S. Tang}, Inverse Probl. 38, No. 1, Article ID 015004, 42 p. (2022; Zbl 1479.94087) Full Text: DOI arXiv
Shi, Chungang; Wang, Wei; Chen, Dafeng Weak time discretization for slow-fast stochastic reaction-diffusion equations. (English) Zbl 1485.60032 Discrete Contin. Dyn. Syst., Ser. B 26, No. 12, 6285-6310 (2021). Reviewer: Stefan Tappe (Freiburg) MSC: 60F10 60H15 35Q55 35K57 35R60 PDFBibTeX XMLCite \textit{C. Shi} et al., Discrete Contin. Dyn. Syst., Ser. B 26, No. 12, 6285--6310 (2021; Zbl 1485.60032) Full Text: DOI
Giunta, Valeria; Lombardo, Maria Carmela; Sammartino, Marco Pattern formation and transition to chaos in a chemotaxis model of acute inflammation. (English) Zbl 1475.92032 SIAM J. Appl. Dyn. Syst. 20, No. 4, 1844-1881 (2021). MSC: 92C17 92C15 35B36 35B32 65P20 PDFBibTeX XMLCite \textit{V. Giunta} et al., SIAM J. Appl. Dyn. Syst. 20, No. 4, 1844--1881 (2021; Zbl 1475.92032) Full Text: DOI
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 PDFBibTeX XMLCite \textit{G. Nadin} et al., J. Math. Biol. 83, No. 2, Paper No. 12, 17 p. (2021; Zbl 1466.92004) Full Text: DOI arXiv
Dyson, Alan Existence and uniqueness of traveling fronts in lateral inhibition neural fields with sigmoidal firing rates. (English) Zbl 1462.35029 SIAM J. Appl. Dyn. Syst. 19, No. 3, 2194-2231 (2020). MSC: 35B25 35C07 35R09 45K05 92C20 PDFBibTeX XMLCite \textit{A. Dyson}, SIAM J. Appl. Dyn. Syst. 19, No. 3, 2194--2231 (2020; Zbl 1462.35029) Full Text: DOI arXiv
Dektor, Alec; Venturi, Daniele Dynamically orthogonal tensor methods for high-dimensional nonlinear PDEs. (English) Zbl 1453.65280 J. Comput. Phys. 404, Article ID 109125, 31 p. (2020). MSC: 65M15 35L50 35K20 PDFBibTeX XMLCite \textit{A. Dektor} and \textit{D. Venturi}, J. Comput. Phys. 404, Article ID 109125, 31 p. (2020; Zbl 1453.65280) Full Text: DOI arXiv
Erhardt, André H.; Mardal, Kent-Andre; Schreiner, Jakob E. Dynamics of a neuron-glia system: the occurrence of seizures and the influence of electroconvulsive stimuli. A mathematical and numerical study. (English) Zbl 1451.92070 J. Comput. Neurosci. 48, No. 2, 229-251 (2020). MSC: 92C20 92C32 92C55 35B32 PDFBibTeX XMLCite \textit{A. H. Erhardt} et al., J. Comput. Neurosci. 48, No. 2, 229--251 (2020; Zbl 1451.92070) Full Text: DOI
Bayani, A.; Dunster, J. L.; Crofts, J. J.; Nelson, M. R. Mechanisms and points of control in the spread of inflammation: a mathematical investigation. (English) Zbl 1437.92016 Bull. Math. Biol. 82, No. 4, Paper No. 45, 22 p. (2020). MSC: 92C17 92C32 35Q92 PDFBibTeX XMLCite \textit{A. Bayani} et al., Bull. Math. Biol. 82, No. 4, Paper No. 45, 22 p. (2020; Zbl 1437.92016) Full Text: DOI
Li, Shihu; Xie, Yingchao Averaging principle for stochastic 3D fractional Leray-\(\alpha\) model with a fast oscillation. (English) Zbl 1447.60109 Stochastic Anal. Appl. 38, No. 2, 248-276 (2020). MSC: 60H15 70K70 35Q30 35R60 PDFBibTeX XMLCite \textit{S. Li} and \textit{Y. Xie}, Stochastic Anal. Appl. 38, No. 2, 248--276 (2020; Zbl 1447.60109) Full Text: DOI
Gnann, Manuel V.; Kuehn, Christian; Pein, Anne Towards sample path estimates for fast-slow stochastic partial differential equations. (English) Zbl 1423.60099 Eur. J. Appl. Math. 30, No. 5, 1004-1024 (2019). MSC: 60H15 35R60 37Hxx PDFBibTeX XMLCite \textit{M. V. Gnann} et al., Eur. J. Appl. Math. 30, No. 5, 1004--1024 (2019; Zbl 1423.60099) Full Text: DOI
Bhattacharya, Sayak; Iglesias, Pablo A. Controlling excitable wave behaviors through the tuning of three parameters. (English) Zbl 1411.92039 Biol. Cybern. 113, No. 1-2, 61-70 (2019). MSC: 92C20 35Q92 PDFBibTeX XMLCite \textit{S. Bhattacharya} and \textit{P. A. Iglesias}, Biol. Cybern. 113, No. 1--2, 61--70 (2019; Zbl 1411.92039) Full Text: DOI
da Silva, Severino Horácio Lower semicontinuity of global attractors for a class of evolution equations of neural fields type in a bounded domain. (English) Zbl 1401.45010 Differ. Equ. Dyn. Syst. 26, No. 4, 371-391 (2018). MSC: 45K05 45M05 35B41 PDFBibTeX XMLCite \textit{S. H. da Silva}, Differ. Equ. Dyn. Syst. 26, No. 4, 371--391 (2018; Zbl 1401.45010) Full Text: DOI arXiv
Kaper, Tasso J.; Vo, Theodore Delayed loss of stability due to the slow passage through Hopf bifurcations in reaction-diffusion equations. (English) Zbl 1397.35137 Chaos 28, No. 9, 091103, 9 p. (2018). MSC: 35K57 35B32 35B35 PDFBibTeX XMLCite \textit{T. J. Kaper} and \textit{T. Vo}, Chaos 28, No. 9, 091103, 9 p. (2018; Zbl 1397.35137) 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
Bilinsky, L. M.; Baer, S. M. Slow passage through a Hopf bifurcation in excitable nerve cables: spatial delays and spatial memory effects. (English) Zbl 1385.92011 Bull. Math. Biol. 80, No. 1, 130-150 (2018). MSC: 92C20 74H60 34E20 35K57 PDFBibTeX XMLCite \textit{L. M. Bilinsky} and \textit{S. M. Baer}, Bull. Math. Biol. 80, No. 1, 130--150 (2018; Zbl 1385.92011) Full Text: DOI
Lombardo, M. C.; Barresi, R.; Bilotta, E.; Gargano, F.; Pantano, P.; Sammartino, M. Demyelination patterns in a mathematical model of multiple sclerosis. (English) Zbl 1378.92034 J. Math. Biol. 75, No. 2, 373-417 (2017). MSC: 92C50 92C17 35Q92 92C40 35B36 PDFBibTeX XMLCite \textit{M. C. Lombardo} et al., J. Math. Biol. 75, No. 2, 373--417 (2017; Zbl 1378.92034) Full Text: DOI
Coutinho, Andréia S.; Pereira, Antônio L. Equivariant bifurcations in a non-local model of ferromagnetic materials. (English) Zbl 1382.82036 Nonlinear Anal., Real World Appl. 37, 1-13 (2017). Reviewer: Claudia Simionescu-Badea (Wien) MSC: 82C32 82C20 35Q82 35B32 81R40 PDFBibTeX XMLCite \textit{A. S. Coutinho} and \textit{A. L. Pereira}, Nonlinear Anal., Real World Appl. 37, 1--13 (2017; Zbl 1382.82036) Full Text: DOI
Chen, Xinfu; Ermentrout, Bard Traveling pulses in a nonlocal equation arising near a saddle-node infinite cycle bifurcation. (English) Zbl 1383.92014 SIAM J. Appl. Math. 77, No. 4, 1204-1229 (2017). MSC: 92B20 92C20 45G10 34B15 35C07 PDFBibTeX XMLCite \textit{X. Chen} and \textit{B. Ermentrout}, SIAM J. Appl. Math. 77, No. 4, 1204--1229 (2017; Zbl 1383.92014) Full Text: DOI
Beck, Margaret Stability of nonlinear waves: pointwise estimates. (English) Zbl 1359.35018 Discrete Contin. Dyn. Syst., Ser. S 10, No. 2, 191-211 (2017). MSC: 35C07 35Kxx 34Dxx 35B35 35E05 PDFBibTeX XMLCite \textit{M. Beck}, Discrete Contin. Dyn. Syst., Ser. S 10, No. 2, 191--211 (2017; Zbl 1359.35018) Full Text: DOI
Ghazaryan, Anna; Lafortune, Stéphane; McLarnan, Peter Combustion waves in hydraulically resistant porous media in a special parameter regime. (English) Zbl 1415.80005 Physica D 332, 23-33 (2016). MSC: 80A25 35B35 35Q79 76S05 PDFBibTeX XMLCite \textit{A. Ghazaryan} et al., Physica D 332, 23--33 (2016; Zbl 1415.80005) Full Text: DOI arXiv
Duanmu, M.; Whitaker, N.; Kevrekidis, P. G.; Vainchtein, A.; Rubin, J. E. Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators. (English) Zbl 1364.34043 Physica D 325, 25-40 (2016). MSC: 34C15 35R10 35C07 34C60 92C30 PDFBibTeX XMLCite \textit{M. Duanmu} et al., Physica D 325, 25--40 (2016; Zbl 1364.34043) 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
Hsu, Ting-Hao Viscous singular shock profiles for a system of conservation laws modeling two-phase flow. (English) Zbl 1347.35166 J. Differ. Equations 261, No. 4, 2300-2333 (2016). Reviewer: Jörg Härterich (Bochum) MSC: 35L67 35L65 34E15 34C37 35B25 PDFBibTeX XMLCite \textit{T.-H. Hsu}, J. Differ. Equations 261, No. 4, 2300--2333 (2016; Zbl 1347.35166) Full Text: DOI arXiv
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
da Silva, Severino H.; Pereira, Antônio L. Asymptotic behavior for a nonlocal model of neural fields. (English) Zbl 1369.35103 São Paulo J. Math. Sci. 9, No. 2, 181-194 (2015). MSC: 35R09 35B41 37B55 PDFBibTeX XMLCite \textit{S. H. da Silva} and \textit{A. L. Pereira}, São Paulo J. Math. Sci. 9, No. 2, 181--194 (2015; Zbl 1369.35103) Full Text: DOI
Ghazaryan, Anna; Lafortune, Stéphane; Manukian, Vahagn Stability of front solutions in a model for a surfactant driven flow on an inclined plane. (English) Zbl 1364.35036 Physica D 307, 1-13 (2015). MSC: 35B35 35Q35 76D08 35C07 PDFBibTeX XMLCite \textit{A. Ghazaryan} et al., Physica D 307, 1--13 (2015; Zbl 1364.35036) Full Text: DOI
Kawamura, Yoji; Nakao, Hiroya Phase description of oscillatory convection with a spatially translational mode. (English) Zbl 1364.76046 Physica D 295-296, 11-29 (2015). MSC: 76D27 76E06 35B06 35B20 35Q35 PDFBibTeX XMLCite \textit{Y. Kawamura} and \textit{H. Nakao}, Physica D 295--296, 11--29 (2015; Zbl 1364.76046) Full Text: DOI arXiv
Horikis, Theodoros P. Dark soliton dynamics under the complex Ginzburg-Landau equation. (English) Zbl 1353.35273 Chaos Solitons Fractals 77, 94-100 (2015). MSC: 35Q56 35C08 PDFBibTeX XMLCite \textit{T. P. Horikis}, Chaos Solitons Fractals 77, 94--100 (2015; Zbl 1353.35273) Full Text: DOI
Provencher Langlois, Gabriel; Farazmand, Mohammad; Haller, George Asymptotic dynamics of inertial particles with memory. (English) Zbl 1361.37070 J. Nonlinear Sci. 25, No. 6, 1225-1255 (2015). MSC: 37N10 35R11 35Q35 34A08 34K37 PDFBibTeX XMLCite \textit{G. Provencher Langlois} et al., J. Nonlinear Sci. 25, No. 6, 1225--1255 (2015; Zbl 1361.37070) Full Text: DOI arXiv
Laing, Carlo R. Exact neural fields incorporating gap junctions. (English) Zbl 1369.92020 SIAM J. Appl. Dyn. Syst. 14, No. 4, 1899-1929 (2015). MSC: 92C20 34C15 34D06 35B36 PDFBibTeX XMLCite \textit{C. R. Laing}, SIAM J. Appl. Dyn. Syst. 14, No. 4, 1899--1929 (2015; Zbl 1369.92020) Full Text: DOI
Ghazaryan, A.; Lafortune, S.; McLarnan, P. Stability analysis for combustion fronts traveling in hydraulically resistant porous media. (English) Zbl 1320.35137 SIAM J. Appl. Math. 75, No. 3, 1225-1244 (2015). MSC: 35C07 34C37 35K55 35K57 35P15 35B35 80A25 34E10 PDFBibTeX XMLCite \textit{A. Ghazaryan} et al., SIAM J. Appl. Math. 75, No. 3, 1225--1244 (2015; Zbl 1320.35137) Full Text: DOI arXiv
Bressloff, Paul C.; Kilpatrick, Zachary P. Nonlinear Langevin equations for wandering patterns in stochastic neural fields. (English) Zbl 1402.92076 SIAM J. Appl. Dyn. Syst. 14, No. 1, 305-334 (2015). MSC: 92C20 35C07 35R60 PDFBibTeX XMLCite \textit{P. C. Bressloff} and \textit{Z. P. Kilpatrick}, SIAM J. Appl. Dyn. Syst. 14, No. 1, 305--334 (2015; Zbl 1402.92076) Full Text: DOI arXiv
Jackson, R. K.; Marangell, R.; Susanto, H. An instability criterion for nonlinear standing waves on nonzero backgrounds. (English) Zbl 1310.35217 J. Nonlinear Sci. 24, No. 6, 1177-1196 (2014). Reviewer: Anthony D. Osborne (Keele) MSC: 35Q55 35C08 35Q41 37K40 PDFBibTeX XMLCite \textit{R. K. Jackson} et al., J. Nonlinear Sci. 24, No. 6, 1177--1196 (2014; Zbl 1310.35217) Full Text: DOI arXiv
Barber, Jared; Tronzo, Mark; Harold Horvat, C.; Clermont, Gilles; Upperman, Jeffrey; Vodovotz, Yoram; Yotov, Ivan A three-dimensional mathematical and computational model of necrotizing enterocolitis. (English) Zbl 1406.92282 J. Theor. Biol. 322, 17-32 (2013). MSC: 92C50 92C17 35Q92 PDFBibTeX XMLCite \textit{J. Barber} et al., J. Theor. Biol. 322, 17--32 (2013; Zbl 1406.92282) Full Text: DOI Link
Nishi, Kei; Nishiura, Yasumasa; Teramoto, Takashi Dynamics of two interfaces in a hybrid system with jump-type heterogeneity. (English) Zbl 1384.37102 Japan J. Ind. Appl. Math. 30, No. 2, 351-395 (2013). MSC: 37L10 35B25 35K40 35K57 PDFBibTeX XMLCite \textit{K. Nishi} et al., Japan J. Ind. Appl. Math. 30, No. 2, 351--395 (2013; Zbl 1384.37102) Full Text: DOI
Kilpatrick, Zachary P.; Ermentrout, G. Bard Hallucinogen persisting perception disorder in neuronal networks with adaptation. (English) Zbl 1446.92058 J. Comput. Neurosci. 32, No. 1, 25-53 (2012). MSC: 92B20 92C50 35C07 PDFBibTeX XMLCite \textit{Z. P. Kilpatrick} and \textit{G. B. Ermentrout}, J. Comput. Neurosci. 32, No. 1, 25--53 (2012; Zbl 1446.92058)
Bressloff, Paul C. From invasion to extinction in heterogeneous neural fields. (English) Zbl 1291.92024 J. Math. Neurosci. 2, Paper No. 6, 27 p. (2012). MSC: 92C20 35Q92 35K57 PDFBibTeX XMLCite \textit{P. C. Bressloff}, J. Math. Neurosci. 2, Paper No. 6, 27 p. (2012; Zbl 1291.92024) Full Text: DOI
Sherratt, Jonathan A.; Smith, Matthew J. Transition to spatiotemporal chaos via stationary branching shocks and holes. (English) Zbl 1253.35172 Physica D 241, No. 20, 1671-1679 (2012). MSC: 35Q56 65P20 PDFBibTeX XMLCite \textit{J. A. Sherratt} and \textit{M. J. Smith}, Physica D 241, No. 20, 1671--1679 (2012; Zbl 1253.35172) Full Text: DOI
Da Silva, Severino Horácio Existence and upper semicontinuity of global attractors for neural network in a bounded domain. (English) Zbl 1257.35048 Differ. Equ. Dyn. Syst. 19, No. 1-2, 87-96 (2011). MSC: 35B41 35R09 35Q92 PDFBibTeX XMLCite \textit{S. H. Da Silva}, Differ. Equ. Dyn. Syst. 19, No. 1--2, 87--96 (2011; Zbl 1257.35048) Full Text: DOI
Consiglieri, Luisa; Domingos, Ana Rute On the sodium concentration diffusion with three-dimensional extracellular stimulation. (English) Zbl 1221.92019 Int. J. Math. Math. Sci. 2011, Article ID 862813, 19 p. (2011). MSC: 92C20 92C37 35Q92 PDFBibTeX XMLCite \textit{L. Consiglieri} and \textit{A. R. Domingos}, Int. J. Math. Math. Sci. 2011, Article ID 862813, 19 p. (2011; Zbl 1221.92019) Full Text: DOI
Reynolds, Angela; Ermentrout, G. Bard; Clermont, Gilles A mathematical model of pulmonary gas exchange under inflammatory stress. (English) Zbl 1406.92115 J. Theor. Biol. 264, No. 2, 161-173 (2010). MSC: 92C30 35Q92 PDFBibTeX XMLCite \textit{A. Reynolds} et al., J. Theor. Biol. 264, No. 2, 161--173 (2010; Zbl 1406.92115) Full Text: DOI Link
Zhang, Linghai; Wu, Ping-Shi; Stoner, Melissa Anne Influence of sodium currents on speeds of traveling wave fronts in synaptically coupled neuronal networks. (English) Zbl 1197.35077 Physica D 239, No. 1-2, 9-32 (2010). MSC: 35C07 35R09 45K05 92B20 PDFBibTeX XMLCite \textit{L. Zhang} et al., Physica D 239, No. 1--2, 9--32 (2010; Zbl 1197.35077) Full Text: DOI
Kevrekidis, Panayotis G. The one-dimensional case. (English) Zbl 1189.37070 Kevrekidis, Panayotis G., The discrete nonlinear Schrödinger equation. Mathematical analysis, numerical computations and physical perspectives. Berlin: Springer (ISBN 978-3-540-89198-7/hbk; 978-3-540-89199-4/ebook). Springer Tracts in Modern Physics 232, 11-53 (2009). Reviewer: Vladimir Răsvan (Craiova) MSC: 37K10 34B30 37K40 35Q55 PDFBibTeX XMLCite \textit{P. G. Kevrekidis}, Springer Tracts Mod. Phys. 232, 11--53 (2009; Zbl 1189.37070) Full Text: DOI
Doelman, Arjen; van Heijster, Peter; Kaper, Tasso J. Pulse dynamics in a three-component system: Existence analysis. (English) Zbl 1173.35068 J. Dyn. Differ. Equations 21, No. 1, 73-115 (2009). Reviewer: Dimitar A. Kolev (Sofia) MSC: 35K55 35B32 34C37 35K45 35B25 92D25 PDFBibTeX XMLCite \textit{A. Doelman} et al., J. Dyn. Differ. Equations 21, No. 1, 73--115 (2009; Zbl 1173.35068) Full Text: DOI
Ivey, T.; Lafortune, S. Spectral stability analysis for periodic traveling wave solutions of NLS and CGL perturbations. (English) Zbl 1148.35086 Physica D 237, No. 13, 1750-1772 (2008). MSC: 35Q55 35Q72 35P05 35B10 35B35 37K45 PDFBibTeX XMLCite \textit{T. Ivey} and \textit{S. Lafortune}, Physica D 237, No. 13, 1750--1772 (2008; Zbl 1148.35086) Full Text: DOI arXiv
Zumbrun, Kevin A sharp stability criterion for soliton-type propagating phase boundaries in Korteweg’s model. (English) Zbl 1187.35229 Z. Anal. Anwend. 27, No. 1, 11-30 (2008). MSC: 35Q53 35B35 35Q51 37K05 76N15 PDFBibTeX XMLCite \textit{K. Zumbrun}, Z. Anal. Anwend. 27, No. 1, 11--30 (2008; Zbl 1187.35229) Full Text: DOI arXiv
Sandstede, Björn Evans functions and nonlinear stability of traveling waves in neuronal network models. (English) Zbl 1144.35342 Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 8, 2693-2704 (2007). MSC: 35B35 35F20 35B20 37L15 92B20 45K05 PDFBibTeX XMLCite \textit{B. Sandstede}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 8, 2693--2704 (2007; Zbl 1144.35342) Full Text: DOI
Howard, Peter Asymptotic behavior near transition fronts for equations of generalized Cahn-Hilliard form. (English) Zbl 1117.35009 Commun. Math. Phys. 269, No. 3, 765-808 (2007). Reviewer: Boris A. Malomed (Tel Aviv) MSC: 35B40 35K30 35Q53 82C26 35K55 PDFBibTeX XMLCite \textit{P. Howard}, Commun. Math. Phys. 269, No. 3, 765--808 (2007; Zbl 1117.35009) Full Text: DOI
Pavliotis, G. A.; Stuart, A. M. Periodic homogenization for inertial particles. (English) Zbl 1100.82023 Physica D 204, No. 3-4, 161-187 (2005). Reviewer: Eckhard Giere (Clausthal-Zellerfeld) MSC: 82C70 82C80 35B27 76M35 76M50 76F25 PDFBibTeX XMLCite \textit{G. A. Pavliotis} and \textit{A. M. Stuart}, Physica D 204, No. 3--4, 161--187 (2005; Zbl 1100.82023) Full Text: DOI arXiv Link
Prat, Alain; Li, Yue-Xian; Bressloff, Paul Inhomogeneity-induced bifurcation of stationary and oscillatory pulses. (English) Zbl 1082.35025 Physica D 202, No. 3-4, 177-199 (2005). Reviewer: Ángel Calsina (Barcelona) MSC: 35B32 35K57 45K05 35C05 35Q80 92C20 PDFBibTeX XMLCite \textit{A. Prat} et al., Physica D 202, No. 3--4, 177--199 (2005; Zbl 1082.35025) Full Text: DOI
Wu, Yaping; Zhao, Xuezhi The existence and stability of travelling waves with transition layers for some singular cross-diffusion systems. (English) Zbl 1144.35412 Physica D 200, No. 3-4, 325-358 (2005). MSC: 35K57 35B25 35B35 35K45 37L99 PDFBibTeX XMLCite \textit{Y. Wu} and \textit{X. Zhao}, Physica D 200, No. 3--4, 325--358 (2005; Zbl 1144.35412) Full Text: DOI
Jalics, Jozsi Slow waves in mutually inhibitory neuronal networks. (English) Zbl 1055.92009 Physica D 192, No. 1-2, 95-122 (2004). MSC: 92C20 35B25 37N25 35F20 45K05 35Q92 PDFBibTeX XMLCite \textit{J. Jalics}, Physica D 192, No. 1--2, 95--122 (2004; Zbl 1055.92009) Full Text: DOI
Zhang, Fu Coexistence of a pulse and multiple spikes and transition layers in the standing waves of a reaction-diffusion system. (English) Zbl 1058.35112 J. Differ. Equations 205, No. 1, 77-155 (2004). Reviewer: Jiaqi Mo (Wuhu) MSC: 35K57 35B25 PDFBibTeX XMLCite \textit{F. Zhang}, J. Differ. Equations 205, No. 1, 77--155 (2004; Zbl 1058.35112) Full Text: DOI
Aranson, Igor S.; Kramer, Lorenz The world of the complex Ginzburg-Landau equation. (English) Zbl 1205.35299 Rev. Mod. Phys. 74, No. 1, 99-143 (2002). MSC: 35Q56 82D50 82D55 PDFBibTeX XMLCite \textit{I. S. Aranson} and \textit{L. Kramer}, Rev. Mod. Phys. 74, No. 1, 99--143 (2002; Zbl 1205.35299) Full Text: DOI arXiv
Howard, Peter Local tracking and stability for degenerate viscous shock waves. (English) Zbl 1019.35064 J. Differ. Equations 186, No. 2, 440-469 (2002). Reviewer: Dimitar A.Kolev (Sofia) MSC: 35L67 35L60 35L65 76L05 35L45 PDFBibTeX XMLCite \textit{P. Howard}, J. Differ. Equations 186, No. 2, 440--469 (2002; Zbl 1019.35064) Full Text: DOI
Lega, Joceline Traveling hole solutions of the complex Ginzburg-Landau equation: A review. (English) Zbl 0977.35023 Physica D 152-153, 269-287 (2001). Reviewer: Aleksander Pankov (Vinnitsa) MSC: 35B35 35K55 35Q55 PDFBibTeX XMLCite \textit{J. Lega}, Physica D 152--153, 269--287 (2001; Zbl 0977.35023) Full Text: DOI
Lin, Xiao-Biao Construction and asymptotic stability of structurally stable internal layer solutions. (English) Zbl 0986.34043 Trans. Am. Math. Soc. 353, No. 8, 2983-3043 (2001). Reviewer: P.Habets (Louvain-La-Neuve) MSC: 34D15 34D30 35B25 35C20 37C29 34C37 34E05 34E15 PDFBibTeX XMLCite \textit{X.-B. Lin}, Trans. Am. Math. Soc. 353, No. 8, 2983--3043 (2001; Zbl 0986.34043) Full Text: DOI
Rubin, J. E. Stability, bifurcations and edge oscillations in standing pulse solutions to an inhomogeneous reaction-diffusion system. (English) Zbl 1089.35511 Proc. R. Soc. Edinb., Sect. A, Math. 129, No. 5, 1033-1079 (1999). MSC: 35K57 37L15 34C23 35B32 37L10 78A55 PDFBibTeX XMLCite \textit{J. E. Rubin}, Proc. R. Soc. Edinb., Sect. A, Math. 129, No. 5, 1033--1079 (1999; Zbl 1089.35511) Full Text: DOI
Kapitula, Todd; Sandstede, Björn Stability of bright solitary-wave solutions to perturbed nonlinear Schrödinger equations. (English) Zbl 0935.35150 Physica D 124, No. 1-3, 58-103 (1998). MSC: 35Q55 37K45 35B35 78A60 PDFBibTeX XMLCite \textit{T. Kapitula} and \textit{B. Sandstede}, Physica D 124, No. 1--3, 58--103 (1998; Zbl 0935.35150) Full Text: DOI