Research Articles
Publications
Calculating Fourier Transforms of
Long-Tailed Functions,
SIAM Journal on Scientific and Statistical Computing,
volume 8 (1987) pages 1005-1111,
with J.N. Lyness
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,
with S. Wiggins
Lobe area in adiabatic Hamiltonian systems,
PhysicaD,
volume 51 (1991) pages 205-212,
with S. Wiggins
On the structure of separatrix-swept regions in
singularly-perturbed
Hamiltonian systems,
Differential and
Integral Equations,
volume 5 (1992) pages 1363-1381,
with 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,
with S. Wiggins
A geometric criterion for adiabatic chaos,
Journal of Mathematical Physics,
volume 35 (1994) pages 1202-1218,
with Gregor Kovacic
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,
with C. Soto-Trevino
A simple model for chaotic advection and scattering,
CHAOS,
volume 5 (1995) pages 671-686,
with Gustavo Stolovitzky and Lawrence Sirovich
Wave-number transport:
scattering of small-scale internal waves by large-scale
wave packets,
Journal of Fluid Mechanics,
volume 289 (1995) pages 379-405,
with David L. Bruhwiler
N-th order split operator schemes and nonreversible systems,
SIAM Journal on Numerical Analysis,
volume 33 (1996) pages 349-367,
with Daniel Goldman
Tracking invariant manifolds up to exponentially
small error,
SIAM Journal on Mathematical Analysis,
volume 27 (1996) pages 558-577,
with Christopher K.R.T. Jones and Nancy Kopell
Multi-bump orbits homoclinic to resonance bands,
Transactions of the American Mathematical
Society,
volume 348 (1996) pages 3835-3887,
with Gregor Kovacic
Higher order Melnikov theory
for adiabatic systems,
Journal of Mathematical Physics,
volume 37 (1996) pages 6220-6249,
with Cristina Soto-Trevino
Global dynamics of a rapidly forced cart and pendulum,
Nonlinear Dynamics,
volume 13 (1997) pages 131-170,
with S. Weibel and J. Baillieul
Pattern formation in the one-dimensional
Gray-Scott model,
Nonlinearity,
volume 10 (1997) pages 523-563,
with Arjen Doelman 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,
with Arjen Doelman and Robert A. Gardner
[ pdf ]
On acoustic cavitation of slightly subcritical bubbles,
Physics of Fluids,
volume 11 (1999) pages 274-287,
with Anthony Harkin 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,
with Arjen Doelman and Robert A. Gardner
[ pdf ]
A reaction-diffusion system with periodic front dynamics,
SIAM Journal on Applied Mathematics,
volume 60(#5) (2000) pages 1601-1638,
with Georgiy Medvedev and Nancy Kopell
[ pdf ]
On axisymmetric traveling waves and radial solutions
of semilinear elliptic equations,
Natural Resource Modeling,
volume 13 (2000) pages 339-388,
with Thomas P. Witelski and Kinya Ono
[ pdf ]
Stationary periodic
patterns in the 1D Gray-Scott model,
Methods and Applications of Analysis,
volume 7(#1) (2000) 105--150,
with David S. Morgan and Arjen Doelman
[ pdf ]
Alpha-frequency rhythms desynchronize over long cortical distances:
a modeling study,
Journal of Computational Neuroscience ,
volume 9(#3) (2000) 271--291,
with Stephanie R. Jones, David J. Pinto and Nancy Kopell
Large stable pulse solutions
in reaction-diffusion equations,
Indiana University Math Journal,
volume 50, #1 (2001) 443--507,
with Arjen Doelman and Robert A. Gardner
[ pdf ]
Critical wave speeds
for a family of scalar reaction diffusion equations,
Applied Mathematics Letters,
volume 14, #1 (2001),
pages 65--73,
with Thomas P. Witelski and Kinya Ono
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,
with Arjen Doelman and Wiktor Eckhaus
[ 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,
with Arjen Doelman and Wiktor Eckhaus
[ 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,
with Arjen Doelman 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,
with Martin Golubitsky and Kresimir Josic
Coupled pulsation and translation of
two gas bubbles in a liquid,
Journal of Fluid Mechanics,
volume 445 (2001),
pages 377--411,
with Anthony Harkin and Ali Nadim
[ pdf ]
Blowup in the nonlinear Schr\"odinger equation
near critical dimension,
Journal of Mathematical Analysis and Applications,
volume 268 (2002),
pages 517--549,
with Vivi Rottsch\"afer
[ pdf ]
Asymptotic analysis
of two reduction methods
for chemical kinetics,
PhysicaD
volume 165 (2002),
pages 66--93,
with Hans 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,
with Vivi Rottsch\"afer
[ 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,
with Arjen Doelman
[ 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,
with Stephanie R. Jones, 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,
with David J. Pinto, Stephanie R. Jones, 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,
with Antonios Zagaris and Hans 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,
with David S. Morgan
[ pdf ]
Fast and slow dynamics
for the computational singular perturbation
method,
SIAM Multiscale Modelling and Simulations
volume 2 (4) (2004), pages 613--638,
with Antonios Zagaris and Hans Kaper
[ pdf ]
Two perspectives on reduction in ordinary differential equations,
Mathematische Nachrichten,
volume 278 (12-13) (2005), pages 1629--1642,
with Antonios Zagaris and Hans Kaper
[ pdf ]
Projecting to a slow manifold:
Singularly perturbed systems and legacy codes,
SIAM Journal on Applied Dynamical Systems,
volume 4 (2005)
711--731,
with C. William Gear, Yannis Kevrekidis, and Antonios Zagaris
[ 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,
with Nikola Popovic
[ pdf ]
A geometric construction of traveling waves
in a bioremediation model,
Journal of Nonlinear Science,
volume 16 (2006)
329--349,
with Margaret Beck and Arjen Doelman
[ pdf ]
Homoclinic bifurcations at the onset of pulse self-replication,
Journal of Differential Equations,
volume 231(1) (2006)
359--423,
with Arjen Doelman 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,
with Freddy Dumortier and Nikola Popovic
[ pdf ]
The critical wave speed
for the FKPP equation with cut-off,
Nonlinearity,
volume 20 (2007) 855--877,
with Freddy Dumortier and Nikola Popovic
[ pdf ]
Nonlinear asymptotic stability of the semi-strong pulse dynamics
in a regularized Gierer-Meinhart model,
SIAM Journal on Mathematical Analysis,
volume 38 (2006) 1760--1787,
with Arjen Doelman 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,
with Leonid Kalachev, Hans 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.
This Focus Issue includes research articles on MMOs and
was edited jointly with Morten Brons and Horacio Rotstein
[ pdf ]
Analysis of a renormalization group method
and normal form theory for perturbed ordinary differential equations,
PhysicaD,
volume 237(8) (2008) pages 1029--1052,
with R.E. Lee DeVille, Anthony Harkin, Matt Holzer, and Kreso Josic
[ pdf ]
Pulse dynamics in a three-component system:
existence analysis,
Journal of Dynamics and Differential Equations,
volume 21(1) (2009) pages 73--115,
with Peter van Heijster and Arjen Doelman
DOI: 10.1007/s10884-008-9125-2
[ 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,
with Peter van Heijster and Arjen Doelman
[ 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,
with Antonios Zagaris, C.W. Gear,
and Yannis 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,
with Peter de Maesschalck and Nikola Popovic
[ pdf ]
Front interactions in a three-component system,
SIAM Journal on Applied Dynamical Systems,
volume 9 (2010) pages 292--332,
DOI: 10.1137/080744785,
with Peter van Heijster, Arjen Doelman, 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
with Peter van Heijster, Arjen Doelman, 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
with G. Nicholas Benes, Anna M. Barry, Mark A. Kramer, and John Burke
Publications in press
Wave speeds for pushed fronts
in scalar reaction-diffusion equations with cut-off,
to appear in RIMS Kokyuroku Bessatsu,
with Freddy Dumortier
Stability and stabilization
of the constrained runs schemes
for equation-free projection to a slow manifold,
to appear in Discrete and Continuous Dynamical Systems - A,
with Antonios Zagaris, Christophe van de Kerckhoeve, C.W. Gear,
and Yannis Kevrekidis
Canards of mixed type in a neural burster,
to appear in Physical Review E ,
with Mathieu Desroches, John Burke, and Mark Kramer
A showcase of torus canards in neuronal bursters,
to appear in J. Math. Neuroscience,
with John Burke, Anna M. Barry, Mathie Desroches, and Mark A. Kramer,
available on arXiv.org, q-bio: 1107.2834
Publications submitted
Geometric desingularization
of a cusp singularity in slow-fast systems
with applications to Zeeman's examples,
submitted to JDE,
with Henk Broer and Martin Krupa
Existence and stability of traveling pulses
in a reaction-diffusion-mechanics system,
submitted to JNLS,
with Matt Holzer and Arjen Doelman
For copies, please e-mail
tasso@math.bu.edu
The above publications
were completed
with support
from the National Science Foundation.
Back to Tasso's Main Page
last modified August, 2011