Research Articles
Publications
1. Calculating Fourier Transforms of
Long-Tailed Functions,
SIAM Journal on Scientific and Statistical Computing,
volume 8 (1987) pages 1005-1111,
with J.N. Lyness
2. 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
3. Lobe area in adiabatic Hamiltonian systems,
PhysicaD,
volume 51 (1991) pages 205-212,
with S. Wiggins
4. 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
5. 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
6. A geometric criterion for adiabatic chaos,
Journal of Mathematical Physics,
volume 35 (1994) pages 1202-1218,
with Gregor Kovacic
7. 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
8. A simple model for chaotic advection and scattering,
CHAOS,
volume 5 (1995) pages 671-686,
with Gustavo Stolovitzky and Lawrence Sirovich
9. 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
10. N-th order split operator schemes and nonreversible systems,
SIAM Journal on Numerical Analysis,
volume 33 (1996) pages 349-367,
with Daniel Goldman
11. 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
12. Multi-bump orbits homoclinic to resonance bands,
Transactions of the American Mathematical
Society,
volume 348 (1996) pages 3835-3887,
with Gregor Kovacic
13. Higher order Melnikov theory
for adiabatic systems,
Journal of Mathematical Physics,
volume 37 (1996) pages 6220-6249,
with Cristina Soto-Trevino
14. Global dynamics of a rapidly forced cart and pendulum,
Nonlinear Dynamics,
volume 13 (1997) pages 131-170,
with S. Weibel and J. Baillieul
15.
Pattern formation in the one-dimensional
Gray-Scott model,
Nonlinearity,
volume 10 (1997) pages 523-563,
with Arjen Doelman and Paul Zegeling
16.
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
17.
On acoustic cavitation of slightly subcritical bubbles,
volume 11 (1999) pages 274-287,
with Anthony Harkin and Ali Nadim
18. 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
19.
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
20. 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
21. 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
22. 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
23.
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
24. 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
25.
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
26.
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
27. 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
28. 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
29. 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
30. 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
31. Asymptotic analysis
of two reduction methods
for chemical kinetics,
PhysicaD
volume 165 (2002),
pages 66--93,
with Hans Kaper
32. 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
33. 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
34. 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
35. 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
36. 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
37. 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
38.
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
39.
Two perspectives on reduction in ordinary differential equations,
Mathematische Nachrichten,
volume 278 (12-13) (2005), pages 1629--1642,
with Antonios Zagaris and Hans Kaper
40.
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
41.
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
42. 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
43. 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
44. 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
45. The critical wave speed
for the FKPP equation with cut-off,
Nonlinearity,
volume 20 (2007) 855--877,
with Freddy Dumortier and Nikola Popovic
46. 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
47. Reduction for Michaelis-Menten-Henri kinetics
in the presence of diffusion,
Electronic Journal of Differential Equations,
volume 16 (2007),
with Leonid Kalachev, Hans Kaper, Nikola Popovic, and Antonios Zagaris
Introduction to Focus Issue:
Mixed-mode oscillations: Experiment, computation, and analysis,
CHAOS,
volume 18 (2008) article number 015101.
This Focus Issue includes 14 research articles on MMOs and
was edited jointly with Morten Brons and Horacio Rotstein
48. 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
Publications in press
Publications submitted
Pulse dynamics in a three-component system:
existence analysis,
submitted to Journal of Dynamics and Differential Equations,
with Peter van Heijster and Arjen Doelman
Pulse dynamics in a three-component system:
stability and bifurcations,
submitted to PhysicaD,
with Peter van Heijster and Arjen Doelman
Stability and stabilization
of the constrained runs schemes
for equation-free projection to a slow manifold,
submitted to Philosophical Transactions of the Royal Society A,
with Antonios Zagaris, Christophe van de Kerckhoeve, C.W. Gear,
adn Yannis Kevrekidis
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 February, 2008