Gregor Kovacic Gregor Kovacic
Associate Professor
Department of Mathematical
Sciences
Rensselaer Polytechnic
Institute
Troy, New York 12180-3590
E-mail: kovacg at rpi dot edu
Telephone: (518) 276-6908
Fax: (518) 276-4824
Ph.D. California Institute of Technology, Applied Mathematics, 1990
Research Interests
Nonlinear evolution equations and their applications to scientific
problems
K. A. Newhall, M. S. Shkarayev, P. R. Kramer, G. Kovacic, and D. Cai [2011]. Synchrony in Stochastically Driven Neuronal Networks with Complex Topologies.
M. S. Shkarayev, G. Kovacic, and D. Cai [2011]. Topological effects on dynamics in complex pulse-coupled networks of integrate-and-fire type.
D. Cai, L. Tao, M. S. Shkarayev, A. V. Rangan, D. W. McLaughlin, and G. Kovacic [2011]. The Role of Fluctuations in Coarse-Grained Descriptions of Neuronal Networks.
M. M. Crosskey, A. T. Nixon, L. M. Schick, and G. Kovacic [2011]. Invisibility Cloaking via Non-Smooth Transformation Optics and Ray Tracing, Phys. Lett. A 375, 1903-1911.
K. A. Newhall, G. Kovacic, P. R. Kramer, and D. Cai [2010]. Cascade-Induced Synchrony in Stochastically-Driven Neuronal Networks, Phys. Rev. E 82, 041903.
K. A. Newhall,
G. Kovacic, P. R. Kramer, D. Zhou, A. V. Rangan, and D. Cai [2010]. Dynamics of Current-Based,
Poisson Driven, Integrate-and-Fire Neuronal Networks,
Comm. Math. Sci.,
8, 541-600.
I. Fatkullin,
G. Kovacic, and E. VandenEijnden [2010]. Reduced dynamics of
stochastically perturbed gradient flows, Comm. Math. Sci., 8, 439-461.
M. S. Shkarayev,
G. Kovacic, A. V. Rangan, and D. Cai [2009]. Architectural and functional connectivity in scale-free
integrate-and-fire networks, Europhys. Lett. 88, 50001.
G. Kovacic, L. Tao, A. V. Rangan, and D. Cai [2009]. Fokker-Planck
Description of Conductance-Based
Integrate-and-Fire Neuronal Networks,
Phys. Rev. E 80, 021904.
A. V. Rangan, L.
Tao, G. Kovacic, and D. Cai [2009]. Large-scale computational
modeling of the primary visual cortex, in
Coherent Behavior in Neuronal Networks, K. Josic, M. Matias, R. Romo, J. Rubin Eds., Springer
Series in Computational Neuroscience , Vol. 3,
Springer-Verlag.
W. Lee, G. Kovacic, and D. Cai [2009].
Renormalized Resonance Quartets in Dispersive Wave Turbulence,
Phys. Rev. Lett. 103,
024502.
A. V. Rangan, L.
Tao, G. Kovacic, and D. Cai [2009]. Multi-scale modeling of the
primary visual cortex, IEEE Engineering in Medicine and Biology
Magazine 28(3), 19-24. A. V. Rangan, G.
Kovacic, and D. Cai [2008]. Kinetic theory for neuronal networks
with fast and slow excitatory conductances driven by the same spike
train, Phys. Rev. E 77, 041915. G. Kovacic, L.
Tao, D. Cai, and M. J. Shelley [2008]. Theoretical analysis of
reverse-time correlation for idealized orientation tuning dynamics,
J. Comput. Neurosci. 25(3), 401-438. J. A. Byrne, G.
Kovacic, and I. R. Gabitov [2003]. Polarization switching of light
interacting with a degenerate two-level optical medium, Physica
D 186, 69-92. R. V. Abramov, G.
Kovacic, and A. J. Majda [2003]. Hamiltonian structure and
statistically relevant conserved quantities for the truncated
Burgers-Hopf equation, Commun. Pure Appl. Math. 56 (1),
1-46. M.
Frankel, G. Kovacic, V. Roytburd, and I. Timofeyev [2000].
Finite-dimensional dynamical system modeling thermal instabilities,
Physica D 137, 295-315. R. Camassa, G.
Kovacic, and S.-K. Tin [1998]. A Melnikov method for homoclinic
orbits with many pulses, Arch. Rat. Mech. Anal. 143,
105-193. A.
B. Aceves, D. D. Holm, G. Kovacic, and I. Timofeyev [1997].
Homoclinic orbits and chaos in a second-harmonic generating optical
cavity, Phys. Lett. A 233, 203-208. T. J. Kaper and
G. Kovacic [1996]. Multi-bump orbits homoclinic to resonance bands,
Trans. AMS 348, 3835-3887. D. D. Holm, G.
Kovacic, and T. A. Wettergren [1996]. Homoclinic orbits in the
Maxwell-Bloch equations with a probe, Phys. Rev. E 54,
243-256.
G. Kovacic and T. A. Wettergren [1996]. Homoclinic orbits in the
dynamics of resonantly driven coupled pendula, ZAMP
47, 221-264. G. Kovacic
[1995]. Singular perturbation theory for homoclinic orbits in a
class of near-integrable dissipative systems, SIAM J. Math.
Anal. 26, 1611-1643. D. D. Holm, G.
Kovacic and T. A. Wettergren [1995]. Near-integrability and chaos in
a resonant-cavity laser model, Phys. Lett. A 200,
299-307.
T. J. Kaper and G. Kovacic [1994]. A geometric criterion for
adiabatic chaos, J. Math. Phys. 35 (3), 1202-1218.
G. Kovacic
[1993]. Singular perturbation theory for homoclinic orbits in a
class of near-integrable Hamiltonian systems, J. Dynamics Diff.
Eqns. 5, 559-597. G. Kovacic [1992]. Dissipative
dynamics of orbits homoclinic to a resonance band, Phys. Lett.
A 167, 143-150. G. Kovacic [1992]. Hamiltonian dynamics
of orbits homoclinic to a resonance band, Phys. Lett. A
167, 137-142. G. Kovacic and S. Wiggins [1992]. Orbits
homoclinic to resonances with an application to chaos in a model of the
forced and damped Sine-Gordon equation, Physica D 57,
185-225. D. D. Holm and G. Kovacic [1992]. Homoclinic chaos in a
laser-matter system, Physica D 56, 270-300. A.
Aceves, D. D. Holm, and G. Kovacic [1992]. Homoclinic chaos due to
competition among degenerate modes in a ring-cavity laser, Phys.
Lett. A 161, 499-505. D. D. Holm, G. Kovacic, and B.
Sundaram [1991]. Chaotic laser-matter interaction, Phys. Lett.
A 154, 346-352. D. D. Holm and G. Kovacic [1991].
Homoclinic chaos for ray optics in a fiber, Physica D
51, 177-188. G. Kovacic [1991]. Lobe area via action formalism
in a class of Hamiltonian systems, Physica D 51,
226-233.
Courses
MATH-6400, Ordinary Differential Equations and Dynamical Systems, Spring 2012.
Links
Discrete
and Continuous Dynamical Systems - Series S, for which I am on the editorial commitee.
CSUMS, research program in Computational and Applied Mathematics for undergraduates at Rensselaer.
Shanghai Jiao-Tong University Applied Mathematics Summer School, June 2010.
Poems by my wife, Miriam Herrera.
RPI
Math
Faculty List