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, G. Kovacic, P. R. Kramer, D. Zhou, A. V. Rangan, and D. Cai [2009]. Dynamics of Current-Based, Poisson Driven, Integrate-and-Fire Neuronal Networks, Comm. Math. Sci., to appear.
I. Fatkullin, G. Kovacic, and E. VandenEijnden [2009]. Reduced dynamics of stochastically perturbed gradient flows, Comm. Math. Sci., to appear.
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-Verlag, to appear.
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.
MATH-4210, Mathematical Analysis II, Spring 2009.
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 and Howard.
Applied Mathematics Days is a two-day workshop series where postdoctoral fellows and graduate students from universities in the Northeast meet to give informal talks about their current research projects. In 2008, it was on Oct 31 and Nov 1. The worshop is open to the public and those interested in pursuing graduate, or postgraduate, research in applied mathematics are particularly encouraged to attend. This conference is part of an NSF funded Research Training Group (RTG) program in applied mathematics.
Poems by my wife, Miriam Herrera.
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