Research Articles
Publications
Calculating Fourier Transforms of
Long-Tailed Functions,
SIAM Journal on Scientific and Statistical Computing,
volume 8 (1987) pages 1005-1011,
J.N. Lyness and Tasso J. Kaper
A commentary `On the periodic solutions of
a forced second order equation' by SP Hastings and JB McLeod,
Journal of Nonlinear Science,
volume 1 (1991) pages 247-253,
Tasso J. Kaper and S. Wiggins
Lobe area in adiabatic Hamiltonian systems,
PhysicaD,
volume 51 (1991) pages 205-212,
Tasso J. Kaper and S. Wiggins
On the structure of separatrix-swept regions in
singularly-perturbed
Hamiltonian systems,
Differential and
Integral Equations,
volume 5 (1992) pages 1363-1381,
Tasso J. Kaper and S. Wiggins
An analytical study of transport in Stokes flows exhibiting
large-scale
chaos in the eccentric journal bearing,
Journal of Fluid Mechanics,
volume 253 (1993) pages 211-243,
Tasso J. Kaper and S. Wiggins
A geometric criterion for adiabatic chaos,
Journal of Mathematical Physics,
volume 35 (1994) pages 1202-1218,
Tasso J. Kaper and Gregor Kovacic
A simple model for chaotic advection and scattering,
CHAOS,
volume 5 (1995) pages 671-686,
Gustavo Stolovitzky, Tasso J. Kaper, and Lawrence Sirovich
Periodic orbits in singularly-perturbed systems,
in Nonlinear dynamics and pattern formation in the natural
environment,
(A. Doelman and A. van Harten, editors), Pitman Research Notes
in Mathematics,
volume 335 (1995) pages 295-314,
Cristina Soto-Trevino and Tasso J. Kaper
Wave-number transport:
scattering of small-scale internal waves by large-scale
wave packets,
Journal of Fluid Mechanics,
volume 289 (1995) pages 379-405,
David L. Bruhwiler and Tasso J. Kaper
N-th order split operator schemes and nonreversible systems,
SIAM Journal on Numerical Analysis,
volume 33 (1996) pages 349-367,
Daniel Goldman and Tasso J. Kaper
Tracking invariant manifolds up to exponentially
small error,
SIAM Journal on Mathematical Analysis,
volume 27 (1996) pages 558-577,
Christopher K.R.T. Jones, Tasso J. Kaper, and Nancy Kopell
Multi-bump orbits homoclinic to resonance bands,
Transactions of the American Mathematical
Society,
volume 348 (1996) pages 3835-3887,
Tasso J. Kaper and Gregor Kovacic
Higher order Melnikov theory
for adiabatic systems,
Journal of Mathematical Physics,
volume 37 (1996) pages 6220-6249,
Cristina Soto-Trevino and Tasso J. Kaper
Global dynamics of a rapidly forced cart and pendulum,
Nonlinear Dynamics,
volume 13 (1997) pages 131-170,
Stephen Weibel, Tasso J. Kaper, and John Baillieul
Pattern formation in the one-dimensional
Gray-Scott model,
Nonlinearity,
volume 10 (1997) pages 523-563,
Arjen Doelman, Tasso J. Kaper, and Paul Zegeling
Stability analysis of singular patterns
in the 1-D Gray-Scott model: A matched
asymptotics approach,
Physica D,
volume 122 (1998) pages 1-36,
Arjen Doelman, Robert A. Gardner, and Tasso J. Kaper
[ pdf ]
On acoustic cavitation of slightly subcritical bubbles,
Physics of Fluids,
volume 11 (1999) pages 274-287,
Anthony Harkin, Tasso J. Kaper, and Ali Nadim
[ pdf ]
Stationary periodic
patterns in the 1D Gray-Scott model,
Methods and Applications of Analysis,
volume 7(#1) (2000) 105--150,
David S. Morgan, Arjen Doelman, and Tasso J. Kaper
[ pdf ]
A reaction-diffusion system with periodic front dynamics,
SIAM Journal on Applied Mathematics,
volume 60(#5) (2000) pages 1601-1638,
Georgiy Medvedev, Tasso J. Kaper, and Nancy Kopell
[ pdf ]
On axisymmetric traveling waves and radial solutions
of semilinear elliptic equations,
Natural Resource Modeling,
volume 13 (2000) pages 339-388,
Thomas P. Witelski, Kinya Ono, and Tasso J. Kaper
[ pdf ]
Alpha-frequency rhythms desynchronize over long cortical distances:
a modeling study,
Journal of Computational Neuroscience ,
volume 9(#3) (2000) 271--291,
Stephanie R. Jones, David J. Pinto, Tasso J. Kaper, and Nancy Kopell
Large stable pulse solutions
in reaction-diffusion equations,
Indiana University Math Journal,
volume 50, #1 (2001) 443--507,
Arjen Doelman, Robert A. Gardner, and Tasso J. Kaper
[ pdf ]
Critical wave speeds
for a family of scalar reaction diffusion equations,
Applied Mathematics Letters,
volume 14, #1 (2001),
pages 65--73,
Thomas P. Witelski, Kinya Ono, and Tasso J. Kaper
Slowly-modulated two-pulse solutions
in the Gray-Scott model I:
Asymptotic construction and stability,
SIAM Journal on Applied Mathematics,
volume 61, #3 (2001),
pages 1080--1102,
Arjen Doelman, Wiktor Eckhaus, and Tasso J. Kaper
[ pdf ]
Slowly-modulated two-pulse solutions
in the Gray-Scott model II:
Geometric theory, bifurcations and splitting dynamics,
SIAM Journal on Applied Mathematics,
volume 61, #6 (2001),
pages 2036--2062,
Arjen Doelman, Wiktor Eckhaus, Tasso J. Kaper
[ pdf ]
Spatially periodic and aperiodic multi-pulse patterns
in the one-dimensional
Gierer-Meinhardt equation,
Methods and Applications of Analysis,
volume 8 (2001),
pages 387--414,
Arjen Doelman, Tasso J. Kaper, and Harmen van der Ploeg
[ pdf ]
An unfolding theory approach to bursting
in fast-slow systems,
in Global Analysis of Dynamical Systems,
A Festschrift/Liber Amicorum dedicated to
Floris Takens for his 60-th birthday,
eds. H. Broer, B. Krauskopf, G. Vegter,
IOP Pub., Bristol
(2001), pages 277--308,
Martin Golubitsky, Kresimir Josic, and Tasso J. Kaper
Coupled pulsation and translation of
two gas bubbles in a liquid,
Journal of Fluid Mechanics,
volume 445 (2001),
pages 377--411,
Anthony Harkin, Tasso J. Kaper, and Ali Nadim
[ pdf ]
A stability index analysis of 1-D patterns of the Gray-Scott model,
Memoirs of the AMS,
volume 155, number 737, (2002),
ISBN 0-8218-2739-1,
Arjen Doelman, Robert A. Gardner, and Tasso J. Kaper
[ pdf ]
Asymptotic analysis
of two reduction methods
for chemical kinetics,
PhysicaD
volume 165 (2002),
pages 66--93,
Hans G. Kaper and Tasso J. Kaper
[ pdf ]
Blowup in the nonlinear Schr\"odinger equation
near critical dimension,
Journal of Mathematical Analysis and Applications,
volume 268 (2002),
pages 517--549,
Vivi Rottsch\"afer and Tasso J. Kaper
[ pdf ]
Geometric theory for multi-bump, self-similar, blowup sloutions
of the cubic nonlinear Schr\"odinger equation,
Nonlinearity,
volume 16 (2003), pages 929--961,
Vivi Rottsch\"afer and Tasso J. Kaper
[ pdf ]
Semi-strong pulse interactions
in a class
of coupled reaction-diffusion equations,
SIAM Journal on Applied Dynamical Systems,
volume 2 (2003), pages 53--96,
Arjen Doelman and Tasso J. Kaper
[ pdf ]
Coordination of cellular pattern-generating circuits
that control limb movements: the sources
of stable differences in intersegmental phases,
Journal of Neuroscience,
volume 23(8) (2003), pages 3457--3469,
Stephanie R. Jones, Tasso J. Kaper, Brian Mulloney, and Nancy Kopell
[ pdf ]
Analysis of state-dependent transitions in frequency and long-distance coordination
in a model oscillatory cortical circuit,
Journal of Computational Neuroscience,
volume 15(2) (2003), pages 283--298,
David J. Pinto, Stephanie R. Jones, Tasso J. Kaper, and Nancy Kopell
[ pdf ]
Analysis of the computational singular perturbation
reduction method for chemical kinetics,
Journal of Nonlinear Science,
volume 14(1) (2004), pages 59--91,
Antonios Zagaris, Hans G. Kaper, and Tasso J. Kaper
[ pdf ]
Axisymmetric ring solutions
of the 2-D Gray-Scott model
and their destabilization into spots,
PhysicaD,
volume 192 (1-2) (2004), pages 33--62,
David S. Morgan and Tasso J. Kaper
[ pdf ]
Fast and slow dynamics
for the computational singular perturbation
method,
SIAM Multiscale Modelling and Simulations
volume 2 (4) (2004), pages 613--638,
Antonios Zagaris, Hans G. Kaper, and Tasso J. Kaper
[ pdf ]
Two perspectives on reduction in ordinary differential equations,
Mathematische Nachrichten,
volume 278 (12-13) (2005), pages 1629--1642,
Antonios Zagaris, Hans G. Kaper, and Tasso J. Kaper
[ pdf ]
Projecting to a slow manifold:
Singularly perturbed systems and legacy codes,
SIAM Journal on Applied Dynamical Systems,
volume 4 (2005)
711--731,
C. William Gear, Tasso J. Kaper, Yannis Kevrekidis, and Antonios Zagaris,
DOI: 10.1137/040608295
[ pdf ]
Rigorous asymptotic expansions
for critical wave speeds
in a family of reaction-diffusion equations
Journal of Dynamics and Differential Equations,
volume 18(1) (2006)
103--139,
Nikola Popovic and Tasso J. Kaper
[ pdf ]
A geometric construction of traveling waves
in a bioremediation model,
Journal of Nonlinear Science,
volume 16 (2006)
329--349,
Margaret Beck, Arjen Doelman, and Tasso J. Kaper
[ pdf ]
Homoclinic bifurcations at the onset of pulse self-replication,
Journal of Differential Equations,
volume 231(1) (2006)
359--423,
Arjen Doelman, Tasso J. Kaper, and Lambertus A. Peletier
[ pdf ]
The asymptotic critical wave speed
in a family of scalar reaction-diffusion equations,
Journal of Mathematical Analysis and Applications,
volume 326 (2007) 1007--1023,
Freddy Dumortier, Nikola Popovic, and Tasso J. Kaper
[ pdf ]
The critical wave speed
for the FKPP equation with cut-off,
Nonlinearity,
volume 20 (2007) 855--877,
Freddy Dumortier, Nikola Popovic, and Tasso J. Kaper
[ pdf ]
Nonlinear asymptotic stability of the semi-strong pulse dynamics
in a regularized Gierer-Meinhart model,
SIAM Journal on Mathematical Analysis,
volume 38 (2007) 1760--1787,
Arjen Doelman, Tasso J. Kaper, and Keith Promislow
[ pdf ]
Reduction for Michaelis-Menten-Henri kinetics
in the presence of diffusion,
Electronic Journal of Differential Equations,
volume 16 (2007) 155--184,
Leonid Kalachev, Hans G. Kaper, Tasso J. Kaper, Nikola Popovic, and Antonios Zagaris
[ pdf ]
Introduction to Focus Issue:
Mixed-mode oscillations: Experiment, computation, and analysis,
CHAOS,
volume 18 (2008) article number 015101.
Morten Brons, Tasso J. Kaper, and Horacio Rotstein (eds.)
[ pdf ]
Analysis of a renormalization group method
and normal form theory for perturbed ordinary differential equations,
PhysicaD,
volume 237(8) (2008) pages 1029--1052,
R.E. Lee DeVille, Anthony Harkin, Matt Holzer, Kreso Josic, and Tasso J. Kaper
[ pdf ]
Pulse dynamics in a three-component system:
existence analysis,
Journal of Dynamics and Differential Equations,
volume 21(1) (2009) pages 73--115,
DOI: 10.1007/s10884-008-9125-2,
Arjen Doelman, Peter van Heijster, and Tasso J. Kaper
[ pdf ]
Pulse dynamics in a three-component system:
stability and bifurcations,
PhysicaD,
volume 237(24) (2008) pages 3335--3368,
DOI: 10.1016/j.physd.2008.07.014,
Peter van Heijster, Arjen Doelman, and Tasso J. Kaper
[ pdf ]
Analysis of the accuracy and convergence
of equation-free projection to a slow manifold,
Modelisation Mathematique et Analyse Numerique,
Mathematical Modeling and Numerical Analysis, M2AN,
volume 43 (2009) pages 757--784,
Antonios Zagaris, C. William Gear, Tasso J. Kaper,
and I.G. Kevrekidis
[ pdf ]
Canards and bifurcation delays
of spatially homogeneous and inhomogeneous types
in reaction-diffusion equations,
Advances in Differential Equations,
volume 14 (2009) pages 943--962,
Peter de Maesschalck, Nikola Popovic, and Tasso J. Kaper
Front interactions in a three-component system,
SIAM Journal on Applied Dynamical Systems,
volume 9 (2010) pages 292--332,
DOI: 10.1137/080744785,
Peter van Heijster, Arjen Doelman, Tasso J. Kaper, and Keith Promislow
[ pdf ]
A geometric approach to bistable front propagation
in scalar reaction-diffusion equations with cut-off,
Physica D ,
volume 239 (2010) pages 1984--1999,
DOI: 10.1016/j.physd.2010.07.008,
with Nikola Popovic and Freddy Dumortier
[ pdf ]
Pinned fronts in heterogeneous media of jump type,
Nonlinearity ,
volume 24 (2011) pages 127-157,
DOI: 10.1088/0951-7715/24/1/007,
Peter van Heijster, Arjen Doelman, Tasso J. Kaper, Yasumasa Nishiura,
and Kei-Ichi Ueda
[ pdf ]
An elementary model of torus canards,
Chaos ,
volume 21 (2011) article 023131 (17 pages),
DOI: 10.1063/1.3592798,
G. Nicholas Benes, Anna M. Barry, Tasso J. Kaper, Mark A. Kramer, and John Burke
[ pdf ]
Canards of mixed type in a neural burster,
Physical Review E , volume 85 (2012) article 021920,
DOI: 10.1103/PhysRevE.85.021920,
Mathieu Desroches, John Burke, Tasso J. Kaper, and Mark Kramer
[ pdf ]
A showcase of torus canards in neuronal bursters,
J. Math. Neuroscience, volume 2 (2012) article number 3, 30 pages,
DOI:10.1186/2190-8567-2-3,
John Burke, Anna M. Barry, Mathieu Desroches, Tasso J. Kaper,
and Mark A. Kramer,
[ pdf ]
Stability and stabilization
of the constrained runs schemes
for equation-free projection to a slow manifold,
Discrete and Continuous Dynamical Systems - A,
volume 32(8) (2012) 2759--2804,
Antonios Zagaris, Christophe van de Kerckhoeve, C. William Gear,
Tasso J. Kaper, and Ioannis G. Kevrekidis
[ pdf ]
Wave speeds for pushed fronts
in scalar reaction-diffusion equations with cut-off,
RIMS Kokyuroku Bessatsu,
volume B31 (2012) 117--134,
Freddy Dumortier and Tasso J. Kaper
[ pdf ]
Existence and stability of traveling pulses
in a reaction-diffusion-mechanics system,
Journal of Nonlinear Science,
volume 23 (2013) 129--177,
DOI: 10.1007/s00332-012-9147-0,
Matt Holzer, Arjen Doelman, and Tasso J. Kaper
[ pdf ]
The dynamics of hybrid metabolic-genetic oscillators
Chaos,
volume 23 (2013) article no. 013132,
Ed Reznik, Tasso J. Kaper, and Daniel Segre
[ pdf ]
Energy transfer between the shape and volume modes
of a nonspherical gas bubble,
Physics of Fluids, ,
volume 25 (2013) article no. 062101,
Anthony Harkin, Tasso J. Kaper, and Ali Nadim
[ pdf ]
Geometric desingularization
of a cusp singularity in slow-fast systems
with applications to Zeeman's examples,
Journal of Dynamics and Differential Equations ,
volume 25 (2013) 925--958,
DOI 10.1007/s10884-013-9322-5,
Henk Broer, Tasso J. Kaper, and Martin Krupa
[ pdf ]
Adiabatic stability under semi-strong interactions: The weakly damped regime,
Indiana University Mathematics Journal,
volume 62 (2013) 1809--1859,
DOI 10.1512/iumj_2013.62.5159,
Thomas Bellsky, Arjen Doelman, Tasso J. Kaper, and Keith Promislow,
[ pdf ]
Mixed-Mode Bursting Oscillations: Dynamics created by a slow passage
through spike-adding canard explosion in a square-wave burster
CHAOS ,
volume 23 (2013) article number 046106,
DOI 1054-1500/2013/23(4)/046106/13/,
Mathieu Desroches, Tasso J. Kaper, and Martin Krupa
[ pdf ]
An analysis of the renormalization group method
for asymptotic expansions
with logarithmic switchback terms,
Advances in Differential Equations,
volume 19 (2014) 245--282,
Matt Holzer and Tasso J. Kaper
Wave speeds for the FKPP equation with enhancement to the reaction
function,
Zeitschrift fuer Angewandte und Mathematische Physik,
volume 66 (2014), 607--629,
DOI: 10.1007/s00033-014-0422-9
Freddy Dumortier and Tasso J. Kaper
[ pdf ]
A computational model of BMP movement in sea urchin embryos,
Journal of Theoretical Biology,
volume 363 (2014) 277-289,
DOI: 10.1016/j.jtbi.2014.08.026
Peter van Heijster, Heather Hardway, Tasso J. Kaper, and Cynthia Bradham
[ pdf ]
A note on a
reaction-diffusion model
describing the bone morphogen protein gradient
in Drosophila embryonic patterning,
in
"Nonlinear Dynamics in Partial Differential Equations",
Advanced Studies in Pure Mathematics,
volume 64
(2015) 209-220,
Mathematical Society of Japan,
Cynthia Bradham, Peter van Heijster, and Tasso J. Kaper.
ISBN 978-4-86497-022-8
Geometry of the computational singular perturbation method,
Mathematical Modeling of Natural Phenomena
,
Cambridge University Press,
volume 10(3) (2015) 16-30,
DOI: 10.1051/mmnp/201510303
Hans G. Kaper, Tasso J. Kaper, and Antonios Zagaris
[ pdf ]
Stabilization of ring dark solitons in Bose-Einstein condensates,
Physical Review A
volume 92 (2015) article no. 033611,
W. Wang, Panos G. Kevrekidis, Ricardo Carretero-Gonzalez, Tasso J. Kaper,
Dimitri J. Franzeskakis,
and M. Ma
From canards of folded singularities to torus canards
in a forced van der Pol equation,
Journal of Nonlinear Science.
volume 26 (2016) 405-451,
John Burke, Mathieu Desroches, Alberto Granados, Tasso J. Kaper,
Martin Krupa, and Theodore Vo,
doi: 10.1007/s00332-015-9279-0
Geometric desingularization of degenerate singularities in the
presence of fast rotation: a new proof of known results for slow passage
through Hopf bifurcations,
Indagationes Mathematicae,
volume 27 (2016) 1184-1203,
Michael G. Hayes, Tasso J. Kaper, Peter Szmolyan,
and Martin Wechselberger,
doi: 10.1016/j.indag.2015.11.005
Amplitude-modulated bursting: a novel class of bursting rhythms,
Physical Review Letters,
volume 117 (2016) article number 268101,
Theodore Vo, Tasso J. Kaper, and Mark Kramer.
Analysis of the Approximate Slow Invariant Manifold Method
for reactive flow equations,
Journal of Mathematical Chemistry,
volume 55 (2017) 1725-1754,
Xiaoxuan Wu and Tasso J. Kaper
DOI: 10.1007/s10910-017-0756-6
Dynamical systems analysis of the Maasch-Saltzman
model for glacial cycles,
Physica D,
volume 359, 2017, pages 1-20,
Hans Engler, Hans G. Kaper, Tasso J. Kaper and Theodore Vo.
DOI: 10.16/j.physd.2017.08.006
Delayed loss of stability
due to slow passage through Hopf bifurcations
in reaction-diffusion equations,
Chaos,
volume 28 (2018) article number 091103,
Theodore Vo and Tasso J. Kaper.
DOI: 10.1063/1.5050508
Modeling the dynamics of glacial cycles,
Mathematics of Planet Earth:
Protecting Our Planet, Learning from the Past, Safeguarding for the Future,
Mathematics of Planet Earth: volume 5,
eds. F. Roberts and H.G. Kaper
pages 3-33, Springer Nature, 2019,
Hans Engler, Hans G. Kaper, Tasso J. Kaper, and Theodore Vo,
ISBN 978-3-030-22044-0.
Multi-Mode Attractors and Spatio-Temporal Canards
PhysicaD,
volume 411 (2020) article number 132544,
Theodore Vo, Richard Bertram, and Tasso J. Kaper.
DOI: 10.1016/j.physd.2020.132544
A new class of chimeras in locally coupled oscillators
with small-amplitude, high-frequency asynchrony
and large-amplitude, low-frequency synchrony,
Chaos,
volume 31 (2021) article number 123111,
Tasso J. Kaper and Theodore Vo.
DOI: 10.1063/5.0067421
Delayed Hopf bifurcation and space-time buffer curves
in the complex Ginzburg-Landau equation,
IMA Journal Applied Mathematics,
volume 87 (2022) 131-186,
Ryan Goh, Tasso J. Kaper, and Theodore Vo.
DOI: 10.1093/imamat/hxac001
Symmetry breaking rhythms in coupled, identical fast-slow oscillators,
Chaos,
volume 33 (2023) 011102,
Naziru M. Awal, Irving R. Epstein, Tasso J. Kaper, and Theodore Vo.
DOI: 10.1063/5.0131305
Fronts in the wake of a parameter ramp: Slow passage through pitchfork and
fold bifurcations,
SIAM Journal on Applied Dynamical Systems,
volume 22 (2023) 2312-2356,
Ryan Goh, Tasso J. Kaper, Arnd Scheel, and Theodore Vo.
DOI: 10.1137/22M1541812
Strong symmetry breaking in coupled, identical Lengyel-Epstein oscillators
via folded singularities,
Journal of Nonlinear Science,
volume 34 (2024) article 53,
Naziru M. Awal, Irving R. Epstein, Tasso J. Kaper, and Theodore Vo.
DOI: 10.1007/s00332-024-10033-7
Pitchfork bifurcation along a slow parameter ramp:
Coherent structures in the critical scaling,
Studies in Applied Mathematics,
online May 11 (2024),
Ryan Goh, Tasso J. Kaper, Arnd Scheel
Strong symmetry breaking rhythms created by folded nodes
in a pair of symmetrically-coupled, identical Koper oscillators,
Chaos,
volume 34 (2024) 053142,
Naziru M. Awal, Irving R. Epstein, Tasso J. Kaper, and Theodore Vo.
DOI: 10.1063/5.0202872
A new class of multi-scale reaction-diffusion equations
with closed-form, low-dimensional, invariant manifolds,
with Xiaoxuan Wu,
AMS Contemporary Mathematics,
volume 806 (2024) 189--209.
DOI: 10.1090/conm/806/16156
Publications in press
Publications submitted
On the existence of and relationship between
canards and torus canards
in forced planar slow/fast equations,
with H. Wang and T. Vo, submitted.
For copies, please e-mail
tasso@math.bu.edu
The above publications
were completed
with support
from the National Science Foundation.
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