Preprints

  1. JJ Bramburger, D Altschuler, CI Avery, T Sangsawang, M Beck, P Carter, and B Sandstede.
    Localized radial roll patterns in higher space dimensions.
  2. X Cao, X Luo, and B Sandstede.
    A functional data method for causal dynamic network modeling of task-related fMRI.
  3. S Iyer and B Sandstede.
    Mixing in reaction-diffusion systems: large phase offsets.
  4. JR Abrams, A Schwartz, MV Ciocanel, A Volkening, and B Sandstede.
    Influenza spread on context-specific social networks.

Peer-reviewed Journal Articles

  1. MV Ciocanel, B Sandstede, SP Jeschonek, and KL Mowry.
    Modeling microtubule-based transport and anchoring of mRNA.
    SIAM Journal on Applied Dynamical Systems (at press).
  2. T Aougab, M Beck, P Carter, S Desai, B Sandstede, M Stadt, and A Wheeler.
    Isolas versus snaking of localized rolls.
    Journal of Dynamics and Differential Equations (at press).
  3. E Makrides and B Sandstede.
    Existence and stability of spatially localized patterns.
    Journal of Differential Equations 266 (2018) 1073-1120.
  4. HM McNamara, S Dodson, Y-L Huang, EW Miller, B Sandstede, and AE Cohen.
    Geometry-dependent instabilities in electrically excitable tissues.
    Cell Systems 7 (2018) 359-370.
  5. B de Rijk and B Sandstede.
    Diffusive stability against nonlocalized perturbations of planar wave trains in reaction-diffusion systems.
    Journal of Differential Equations 265 (2018) 5315-5351.
  6. A Volkening and B Sandstede.
    Iridophores as a source of robustness in zebrafish stripes and variability in Danio patterns.
    Nature Communications 9 (2018) 3231.
  7. P Carter and B Sandstede.
    Unpeeling a homoclinic banana in the FitzHugh-Nagumo system.
    SIAM Journal on Applied Dynamical Systems 17 (2018) 236–349.
  8. B Barker, R Nguyen, B Sandstede, N Ventura, and C Wahl.
    Computing Evans functions numerically via boundary-value problems.
    Physica D 367 (2018) 1–10.
  9. V Ciocanel, JA Kreiling, JA Gagnon, KL Mowry, and B Sandstede.
    Analysis of active transport by fluorescence recovery after photobleaching.
    Biophysical Journal 112 (2017) 1714-1725.
  10. C Xia, C Cochrane, J DeGuire, G Fan, E Holmes, M McGuirl, P Murphy, J Palmer, P Carter, L Slivinski, and B Sandstede.
    Assimilating Eulerian and Lagrangian data in traffic-flow models.
    Physica D 346 (2017) 59-72.
  11. P Carter, B de Rijk, and B Sandstede.
    Stability of traveling pulses with oscillatory tails in the FitzHugh-Nagumo system.
    Journal of Nonlinear Science 26 (2016) 1369–1444.
  12. EA Powrie, V Ciocanel, JA Kreiling, JA Gagnon, B Sandstede, and KL Mowry.
    Using in vivo imaging to measure RNA mobility in Xenopus laevis oocytes.
    Methods 98 (2016) 60-65.
  13. B Sandstede and T Theerakarn.
    Regularity of center manifolds via the graph transform.
    Journal of Dynamics and Differential Equations 27 (2015) 989-1006.
  14. A Volkening and B Sandstede.
    Modelling stripe formation in zebrafish: an agent-based approach.
    Journal of the Royal Society Interface 12 (2015) 20150812.
  15. J Guckenheimer, B Krauskopf, HM Osinga and B Sandstede.
    Invariant manifolds and global bifurcations.
    Chaos 25 (2015) 097604.
  16. P Carter and B Sandstede.
    Fast pulses with oscillatory tails in the FitzHugh-Nagumo system.
    SIAM Journal on Mathematical Analysis 47 (2015) 3285-3441.
  17. L Slivinski, E Spiller, A Apte, and B Sandstede.
    A hybrid particle-ensemble Kalman filter for Lagrangian data assimilation.
    Monthly Weather Review 143 (2015) 195–211.
  18. P Carter, PL Christiansen, YB Gaididei, C Gorria, B Sandstede, MP Sorensen, and J Starke.
    Multi-jam solutions in traffic models with velocity-dependent driver strategies.
    SIAM Journal on Applied Mathematics 74 (2014) 1895–1918.
  19. K McQuighan and B Sandstede.
    Oscillons in the planar Ginzburg-Landau equation with 2:1 forcing.
    Nonlinearity 27 (2014) 3073-3116.
  20. M Beck, T Nguyen, B Sandstede and K Zumbrun.
    Nonlinear stability of source defects in the complex Ginzburg-Landau equation.
    Nonlinearity 27 (2014) 739-786.
  21. P van Heijster and B Sandstede.
    Bifurcations to travelling planar spots in a three-component FitzHugh-Nagumo system.
    Physica D 275 (2014) 19-34.
  22. E Makrides and B Sandstede.
    Predicting the bifurcation structure of localized snaking patterns.
    Physica D 268 (2014) 59-78.
  23. S McCalla and B Sandstede.
    Spots in the Swift-Hohenberg equation.
    SIAM Journal on Applied Dynamical Systems 12 (2013) 831-877.
  24. HJ Hupkes and B Sandstede.
    Stability of pulse solutions for the discrete FitzHugh-Nagumo system.
    Transactions of the American Mathematical Society 365 (2013) 251-301.
  25. B Sandstede and Y Xu.
    Snakes and isolas in non-reversible conservative systems.
    Dynamical Systems 27 (2012) 317-329.
  26. P van Heijster and B Sandstede.
    Coexistence of stable spots and fronts in a three-component FitzHugh-Nagumo system.
    RIMS Kokyuroku Bessatsu B31 (2012) 135-155.
  27. B Sandstede, A Scheel, G Schneider and H Uecker.
    Diffusive mixing of periodic wave trains in reaction-diffusion systems.
    Journal of Differential Equations 252 (2012) 3541-3574.
  28. M Beck, T Nguyen, B Sandstede and K Zumbrun.
    Toward nonlinear stability of sources via a modified Burgers equation.
    Physica D 241 (2012) 382-392.
  29. P van Heijster and B Sandstede.
    Planar radial spots in a three-component FitzHugh-Nagumo system.
    Journal of Nonlinear Science 21 (2011) 705-745.
  30. HJ Hupkes, D Pelinovsky and B Sandstede.
    Propagation failure in the discrete Nagumo equation.
    Proceedings of the American Mathematical Society 139 (2011) 3537-3551.
  31. J Knobloch, DJB Lloyd, B Sandstede and T Wagenknecht.
    Isolas of 2-pulse solutions in homoclinic snaking scenarios.
    Journal of Dynamics and Differential Equations 23 (2011) 93-114.
  32. G Derks, S Maad and B Sandstede.
    Perturbations of embedded eigenvalues for the planar bilaplacian.
    Journal of Functional Analysis 260 (2011) 340-398.
  33. HJ Hupkes and B Sandstede.
    Travelling pulses for the discrete FitzHugh-Nagumo system.
    SIAM Journal on Applied Dynamical Systems 9 (2010) 827-882.
  34. D Avitabile, DJB Lloyd, J Burke, E Knobloch and B Sandstede.
    To snake or not to snake in the planar Swift-Hohenberg equation.
    SIAM Journal on Applied Dynamical Systems 9 (2010) 704-733.
  35. S McCalla and B Sandstede. Snaking of radial solutions of the multi-dimensional Swift-Hohenberg equation: a numerical study. Physica D 239 (2010) 1581-1592.
  36. D Obeid, JM Kosterlitz and B Sandstede.
    State selection in the noisy stabilized Kuramoto-Sivashinsky equation.
    Physical Review E 81 (2010) 066205.
  37. M Beck, B Sandstede and K Zumbrun.
    Nonlinear stability of time-periodic viscous shocks.
    Archive for Rational Mechanics and Analysis 196 (2010) 1011-1076.
  38. M Beck, HJ Hupkes, B Sandstede and K Zumbrun.
    Nonlinear stability of semidiscrete shocks for two-sided schemes.
    SIAM Journal on Mathematical Analysis 42 (2010) 857-903.
  39. M Oh and B Sandstede.
    Evans functions for periodic waves on infinite cylindrical domains.
    Journal of Differential Equations 248 (2010) 544-555.
  40. V Manukian, N Costanzino, CKRT Jones and B Sandstede.
    Existence of multi-pulses of the regularized short-pulse and Ostrovsky equations.
    Journal of Dynamics and Differential Equations 21 (2009) 607-622.
  41. HJ Hupkes and B Sandstede.
    Modulated wave trains in lattice differential systems.
    Journal of Dynamics and Differential Equations 21 (2009) 417-485.
  42. V Manukian and B Sandstede.
    Multi-hump pulses in systems with reflection and phase invariance.
    Journal of Differential Equations 247 (2009) 1866-1898.
  43. M Beck, J Knobloch, DJB Lloyd, B Sandstede and T Wagenknecht.
    Snakes, ladders, and isolas of localised patterns.
    SIAM Journal on Mathematical Analysis 41 (2009) 936-972.
  44. A Doelman, B Sandstede, A Scheel and G Schneider.
    The dynamics of modulated wave trains.
    Memoirs of the American Mathematical Society 199(934) (2009).
  45. M Beck, A Ghazaryan and B Sandstede.
    Nonlinear convective stability of travelling fronts near Turing and Hopf instabilities.
    Journal of Differential Equations 246 (2009) 4371-4390.
  46. BG Bale, N Kutz and B Sandstede.
    Optimizing waveguide array mode-locking for high-power fiber lasers.
    IEEE Journal of Selected Topics in Quantum Electronics 15 (2009) 210-231.
  47. DJB Lloyd and B Sandstede.
    Localized radial solutions of the Swift-Hohenberg equation.
    Nonlinearity 22 (2009) 485-524.
  48. DJB Lloyd, B Sandstede, D Avitabile and AR Champneys.
    Localized hexagon patterns of the planar Swift-Hohenberg equation.
    SIAM Journal on Applied Dynamical Systems 7 (2008) 1049-1100.
  49. G Derks, S Maad and B Sandstede.
    Perturbations of embedded eigenvalues for the bilaplacian on a cylinder.
    Discrete and Continuous Dynamical Systems A 21 (2008) 801-821.
  50. B Sandstede and A Scheel.
    Hopf bifurcation from viscous shock waves.
    SIAM Journal on Mathematical Analysis 39 (2008) 2033-2052.
  51. N Kutz and B Sandstede.
    Theory of passive harmonic mode-locking using waveguide arrays.
    Optics Express 16 (2008) 636-650.
  52. B Sandstede and A Scheel.
    Relative Morse indices, Fredholm indices, and group velocities.
    Discrete and Continuous Dynamical Systems A 20 (2008) 139-158.
  53. B Sandstede.
    Evans functions and nonlinear stability of travelling waves in neuronal network models.
    International Journal of Bifurcation and Chaos 17 (2007) 2693-2704.
  54. B Sandstede and A Scheel.
    Period doubling of spiral waves and defects.
    SIAM Journal on Applied Dynamical Systems 6 (2007) 494-547.
  55. A Ghazaryan and B Sandstede.
    Nonlinear convective instability of Turing-unstable fronts near onset: A case study.
    SIAM Journal on Applied Dynamical Systems 6 (2007) 319-347.
  56. JDM Rademacher, B Sandstede and A Scheel. Computing absolute and essential spectra using continuation.
    Physica D 229 (2007) 166-183.
  57. J Humpherys, B Sandstede and K Zumbrun. Efficient computation of analytic bases in Evans function analysis of large systems.
    Numerische Mathematik 103 (2006) 631-642.
  58. B Sandstede and A Scheel.
    Curvature effects on spiral spectra: Generation of point eigenvalues near branch points.
    Physical Review E 73 (2006) 016217.
  59. G Samaey and B Sandstede.
    Determining stability of pulses for partial differential equations with time delays.
    Dynamical Systems 20 (2005) 201-222.
  60. T Kapitula, PG Kevrekidis and B Sandstede.
    Addendum: Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems.
    Physica D 201 (2005) 199-201.
  61. E Grenier, CKRT Jones, F Rousset and B Sandstede.
    Viscous perturbations of marginally stable Euler flow and finite-time Melnikov theory.
    Nonlinearity 18 (2005) 465-483.
  62. B Sandstede and A Scheel.
    Basin boundaries and bifurcations near convective instabilities: A case study.
    Journal of Differential Equations 208 (2005) 176-193.
  63. B Sandstede and A Scheel.
    Absolute instabilities of standing pulses.
    Nonlinearity 18 (2005) 331-378.
  64. T Kapitula, N Kutz and B Sandstede.
    The Evans function for nonlocal equations.
    Indiana University Mathematics Journal 53 (2004) 1095-1126.
  65. T Kapitula, PG Kevrekidis and B Sandstede.
    Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems.
    Physica D 195 (2004) 263-282.
  66. MD Groves and B Sandstede.
    A plethora of three-dimensional periodic travelling gravity-capillary water waves with multipulse transverse profiles.
    Journal of Nonlinear Science 14 (2004) 297-340.
  67. B Sandstede and A Scheel.
    Evans function and blow-up methods in critical eigenvalue problems..
    Discrete and Continuous Dynamical Systems 10 (2004) 941-964.
  68. B Sandstede and A Scheel.
    Defects in oscillatory media: toward a classification.
    SIAM Journal on Applied Dynamical Systems 3 (2004) 1-68.
  69. A Doelman, B Sandstede, A Scheel and G Schneider.
    Propagation of hexagonal patterns near onset.
    European Journal of Applied Mathematics 14 (2003) 85-110.
  70. J Härterich, B Sandstede and A Scheel.
    Exponential dichotomies for linear non-autonomous functional differential equations of mixed type.
    Indiana University Mathematics Journal 51 (2002) 1081-1109.
  71. J O’Neil, N Kutz and B Sandstede.
    Theory and simulations of the dynamics and stability of actively modelocked lasers.
    IEEE Journal of Quantum Electronics 38 (2002) 1412-1419.
  72. T Kapitula, N Kutz and B Sandstede.
    Stability of pulses in the master-modelocking equation.
    Journal of the Optical Society of America B 19 (2002) 740-746.
  73. T Kapitula and B Sandstede.
    Edge bifurcations for near integrable systems via Evans function techniques.
    SIAM Journal on Mathematical Analysis 33 (2002) 1117-1143.
  74. B Sandstede and A Scheel.
    On the structure of spectra of modulated travelling waves.
    Mathematische Nachrichten 232 (2001) 39-93.
  75. R Moore, WL Kath, B Sandstede, CKRT Jones and JC Alexander.
    Stability of multiple pulses in optical fibers with phase-sensitive amplification and noise.
    Optics Communications 195 (2001) 127-139.
  76. B Sandstede and A Scheel.
    Essential instabilities of fronts: bifurcation, and bifurcation failure.
    Dynamical Systems 16 (2001) 1-28.
  77. B Sandstede and A Scheel.
    On the stability of periodic travelling waves with large spatial period.
    Journal of Differential Equations 172 (2001) 134-188.
  78. B Sandstede and A Scheel.
    Superspiral structures of meandering and drifting spiral waves.
    Physical Review Letters 86 (2001) 171-174.
  79. B Sandstede and A Scheel.
    Absolute and convective instabilities of waves on unbounded and large bounded domains.
    Physica D 145 (2000) 233-277.
  80. B Sandstede and A Scheel.
    Absolute versus convective instability of spiral waves.
    Physical Review E 62 (2000) 7708-7714.
  81. B Sandstede.
    Center manifolds for homoclinic solutions.
    Journal of Dynamics and Differential Equations 12 (2000) 449-510.
  82. B Sandstede and A Scheel.
    Gluing unstable fronts and backs together can produce stable pulses.
    Nonlinearity 13 (2000) 1465-1482.
  83. B Sandstede, S Balasuriya, CKRT Jones and P Miller.
    Melnikov theory for finite-time vector fields.
    Nonlinearity 13 (2000) 1357-1377.
  84. GJ Lord, D Peterhof, B Sandstede and A Scheel.
    Numerical computation of solitary waves in infinite cylindrical domains.
    SIAM Journal on Numerical Analysis 37 (2000) 1420-1454.
  85. B Sandstede and A Scheel.
    Spectral stability of modulated travelling waves bifurcating near essential instabilities.
    Proceedings of the Royal Society of Edinburgh A 130 (2000) 419-448.
  86. AC Yew, B Sandstede and CKRT Jones.
    Instability of multiple pulses in coupled nonlinear Schrödinger equations.
    Physical Review E 61 (2000) 5886-5892.
  87. B Sandstede and A Scheel.
    Essential instability of pulses and bifurcations to modulated travelling waves.
    Proceedings of the Royal Society of Edinburgh A 129 (1999) 1263-1290.
  88. D Peterhof and B Sandstede.
    All-optical clock recovery using multisection distributed-feedback lasers.
    Journal of Nonlinear Science 9 (1999) 575-613.
  89. B Sandstede, A Scheel and C Wulff.
    Bifurcations and dynamics of spiral waves.
    Journal of Nonlinear Science 9 (1999) 439-478.
  90. T Kapitula and B Sandstede.
    Stability of bright solitary-wave solutions to perturbed nonlinear Schrödinger equations.
    Physica D 124 (1998) 58-103.
  91. T Kapitula and B Sandstede.
    Instability mechanism for bright solitary-wave solutions to the cubic-quintic Ginzburg-Landau equation.
    Journal of the Optical Society of America B 15 (1998) 2757-2762.
  92. U Bandelow, L Recke and B Sandstede.
    Frequency regions for forced locking of self-pulsating multi-section DFB lasers.
    Optics Communications 147 (1998) 212-218.
  93. S Balasuriya, CKRT Jones and B Sandstede.
    Viscous perturbations of vorticity-conserving flows and separatrix splitting.
    Nonlinearity 11 (1998) 47-77.
  94. B Sandstede.
    Stability of multiple-pulse solutions.
    Transactions of the American Mathematical Society 350 (1998) 429-472.
  95. B Sandstede.
    Stability of N-fronts bifurcating from a twisted heteroclinic loop and an application to the FitzHugh-Nagumo equation.
    SIAM Journal on Mathematical Analysis 29 (1998) 183-207.
  96. B Sandstede, A Scheel and C Wulff.
    Dynamics of spiral waves on unbounded domains using center-manifold reductions.
    Journal of Differential Equations 141 (1997) 122-149.
  97. D Peterhof, B Sandstede and A Scheel.
    Exponential dichotomies for solitary-wave solutions of semilinear elliptic equations on infinite cylinders.
    Journal of Differential Equations 140 (1997) 266-308.
  98. B Sandstede.
    Instability of localized buckling modes in a one-dimensional strut model.
    Philosophical Transactions of the Royal Society of London A 355 (1997) 2083-2097.
  99. B Sandstede.
    Convergence estimates for the numerical approximation of homoclinic solutions.
    IMA Journal of Numerical Analysis 17 (1997) 437-462.
  100. B Sandstede, CKRT Jones and JC Alexander.
    Existence and stability of N-pulses on optical fibers with phase-sensitive amplifiers.
    Physica D 106 (1997) 167-206.
  101. B Sandstede.
    Constructing dynamical systems having homoclinic bifurcation points of codimension two..
    Journal of Dynamics and Differential Equations 9 (1997) 269-288.
  102. JC Alexander, MG Grillakis, CKRT Jones and B Sandstede.
    Stability of pulses on optical fibers with phase-sensitive amplifiers.
    Zeitschrift für Angewandte Mathematik und Physik 48 (1997) 175-192.
  103. B Sandstede, A Scheel and C Wulff.
    Center-manifold reduction for spiral waves.
    Comptes Rendus de l’Académie des Sciences I 324 (1997) 153-158.
  104. M Krupa, B Sandstede and P Szmolyan.
    Fast and slow waves in the FitzHugh-Nagumo equation.
    Journal of Differential Equations 133 (1997) 49-97.
  105. B Fiedler, B Sandstede, A Scheel and C Wulff.
    Bifurcation from relative equilibria of noncompact group actions: skew products, meanders, and drifts.
    Documenta Mathematica 1 (1996) 479-505.
  106. AR Champneys, YA Kuznetsov and B Sandstede.
    A numerical toolbox for homoclinic bifurcation analysis.
    International Journal of Bifurcation and Chaos 6 (1996) 867-887.
  107. AR Champneys, J Härterich and B Sandstede.
    A non-transverse homoclinic orbit to a saddle-node equilibrium.
    Ergodic Theory & Dynamical Systems 16 (1996) 431-450.
  108. B Sandstede and A Scheel.
    Forced symmetry breaking of homoclinic cycles.
    Nonlinearity 8 (1995) 333-365.
  109. B Sandstede and B Fiedler.
    Dynamics of periodically forced parabolic equations on the circle.
    Ergodic Theory & Dynamical Systems 12 (1992) 559-571.
  110. P Brunovský, P Polácik and B Sandstede.
    Convergence in general periodic parabolic equations in one space dimension.
    Nonlinear Analysis (Theory, Methods & Applications) 18 (1992) 209-215.
Interface Cover Photo
Cell Systems Cover Photo

Review and survey articles

  1. B Sandstede.
    Computational Dynamics.
    Encyclopedia of Applied and Computational Mathematics (Edited by B Enquist).
    Springer (2015) 262-266.
  2. AJ Homburg and B Sandstede.
    Homoclinic and heteroclinic bifurcations in vector fields.
    Handbook of Dynamical Systems III (Edited by H Broer, F Takens and B Hasselblatt).
    Elsevier (2010) 379-524.
  3. AR Champneys and B Sandstede.
    Numerical computation of coherent structures.
    In: Numerical Continuation Methods for Dynamical Systems (B Krauskopf, HM Osinga and J Galan-Vioque, eds.).
    Springer (2007) 331-358.
  4. B Sandstede.
    The Evans function.
    In: Encyclopedia of Nonlinear Science (A Scott, ed.).
    Routledge (2005) 278-279.
  5. T Kapitula and B Sandstede.
    Eigenvalues and resonances using the Evans function.
    Discrete and Continuous Dynamical Systems A 10 (2004) 857-869.
  6. WJ Beyn, A Champneys, E Doedel, W Govaerts, YA Kuznetsov and B Sandstede.
    Numerical continuation, and computation of normal forms.
    In: Handbook of Dynamical Systems II (B Fiedler, ed.).
    North-Holland (2002) 149-219.
  7. B Sandstede.
    Stability of travelling waves.
    In: Handbook of Dynamical Systems II (B Fiedler, ed.).
    North-Holland (2002) 983-1055.
  8. B Sandstede, A Scheel and C Wulff.
    Dynamical behavior of patterns with Euclidean symmetry.
    In: Pattern Formation in Continuous and Coupled Systems (M Golubitsky, D Luss and S Strogatz, eds.).
    Springer, IMA Volumes in Mathematics and its Applications 115 (1999) 249-264.

Books Edited

  • Patterns of Dynamics.
    P Gurevich, J Hell, B Sandstede, and A Scheel (Editors).
    Springer Proceedings in Mathematics & Statistics 205 (2017).

Peer-reviewed Papers in Conference Proceedings

  • B Sandstede.
    Homoclinic flip bifurcations in conservative reversible systems.
    In: Recent Trends in Dynamical Systems.
    Springer (2013) 107-124.
  • B Sandstede and A Scheel.
    Absolute and convective stability in large domains.
    In: International Conference on Differential Equations, Berlin 1999.
    World Sci. Publishing 1 (2000) 797-800.
  • R Moore, WL Kath, B Sandstede, CKRT Jones and JC Alexander.
    Stable multiple pulses in optical fibers with phase-sensitive amplification.
    In: Nonlinear guided waves and their applications.
    Optical Society of America, Technical Digest Series 5 (1998) 264-266.
  • D Peterhof, L Recke and B Sandstede.
    On frequency locking of self-pulsating two-section DFB lasers.
    In: Self-organization in activator-inhibitor systems: semiconductors, gas-discharge and chemical active media (H Engel, FJ Niedernostheide, HG Purwins and E Schöll, eds.).
    Wissenschaft und Technik Verlag (1996) 218-222.
  • B Sandstede.
    Asymptotic behavior of solutions of nonautonomous scalar reaction-diffusion equations.
    In: International Conference on Differential Equations, Barcelona 1991 (C Perello, C Simo and J Sola-Morales, eds.).
    World Sci. Publishing 2 (1993) 888-892.

Technical Reports

Theses