Preprints

  1. T. Kolokolnikov and J. Wei, Basic mechanisms driving complex spike dynamics in a chemotaxis model with logistic growth.
  2. Andrea L. Bertozzi, James von Brecht and Hui Sun, T. Kolokolnikov and David Uminsky, Ring Patterns and Their Bifurcations in a Nonlocal Model of Biological Swarms, submitted, CMS.
  3. Sorathan Chaturapruek, Jonah Breslau, Daniel Yazdi, Theodore Kolokolnikov and Scott G. McCalla, Crime Modeling with Levy Flights , submitted to SIAM J. Appl. Math.
  4. T. Kolokolnikov and Alan Lindsay, Recovering multiple small inclusions inside an arbitrary domain in three dimensions using a single measurement

Papers

  1. Yuxin Chen, T. Kolokolnikov and Daniel Zhirov, Collective behavior of large number of vortices in the plane , to appear, Proceedings of the Royal Society A
  2. Theodore Kolokolnikov, Juncheng Wei and Wen Yang, On Large ring solutions for Gierer-Meinhardt system in R3, to appear, JDE.
  3. J. von Brecht, T. Kolokolnikov, A.L. Bertozzi and H. Sun, Swarming on Random Graphs , to appear, J.Stat.Phys.
  4. Chiun-Chuan Chen and T. Kolokolnikov, Simple pde model of spot replication in any dimension, SIAM Journal of Mathematical Analysis, 44(5), pp.3564-3593 (2012)
  5. T. Kolokolnikov, M.J. Ward and J. Wei, The Stability of Steady-State Hot-Spot Patterns for a Reaction-Diffusion Model of Urban Crime, to appear, DCDS-B.
  6. T. Kolokolnikov, Y. Huang and M. Pavlovski, Singular patterns for an aggregation model with a confining potential, to appear, Physica D.
  7. Rebecca McKay Theodore Kolokolnikov and Paul Muir, Interface oscillations in reaction-diffusion systems beyond the Hopf bifurcation , DCDS-B, 17(7), pp. 2523-2543, 2012.
  8. Wangyi Liu, Andrea L. Bertozzi, and Theodore Kolokolnikov, Diffuse interface surface tension models in an expanding flow , Comm. Math. Sci., 10(1), pp. 387-418, 2012.
  9. James von Brecht, David Uminsky, Theodore Kolokolnikov and Andrea L. Bertozzi, Predicting pattern formation in particle interactions , M3AS, vol. 22, Supp. 1, 1140002, 2012
  10. T. Kolokolnikov, Hui Sun, David Uminsky and Andrea L. Bertozzi, Stability of ring patterns arising from two-dimensional particle interactions Phys. Rev. E 84, 015203(R) (2011)
  11. R. C. Fetecau, Y. Huang and T. Kolokolnikov, Swarm dynamics and equilibria for a nonlocal aggregation model Nonlinearity, Vol. 24, No. 10, pp. 2681-2716 (2011).
  12. T. Kolokolnikov and Juncheng Wei, Stability of spiky solutions in a competition model with cross-diffusion , SIAM J. Appl. Math. 71, pp. 1428-1457 (2011).
  13. Rebecca McKay and Theodore Kolokolnikov, Stability transitions and dynamics of localized patterns near the shadow limit of reaction-diffusion systems , DCDS-B, 17(1), pp. 191-220 (2012)
  14. Sina Adl, David Iron and T. Kolokolnikov, A threshold area ratio of organic to conventional agriculture causes recurrent pathogen outbreaks in organic agriculture , Science of The Total Environment 409(11):2192-2197, 2011.
  15. T. Kolokolnikov and Xiaofeng Ren Smoke-ring solutions of Gierer-Meinhardt System in R3 , SIAM Journal on Applied Dynamical Systems 10(1):251-277, 2011.
  16. Adam Alcolado, T. Kolokolnikov and David Iron, Instability thresholds in the microwave heating model with exponential nonlinearity, European Journal of Applied Mathematics, 22(3):187-216, 2011.
  17. M. J. Ward, Samara Pillay, Anthony Peirce and T. Kolokolnikov, An Asymptotic Analysis of the Mean First Passage Time for Narrow Escape Problems: Part I: Two-Dimensional Domains SIAM J. on Multiscale Modelling and Simulation, 8(3):803-835, 2010.
  18. T. Kolokolnikov, Book review: Mathematics and Technology by Christiane Rousseau and Yvan Saint-Aubin , CMS notes, vol. 41 no. 2 March 2009
  19. T. Kolokolnikov, Juncheng Wei and Matthias Winter, Existence and stability analysis of spiky solutions for the gierer-meinhardt system with large reaction rates, Physica D: Nonlinear Phenomena Volume 238(16) 2009, Pages 1695-1710
  20. T. Kolokolnikov, Chunhua Ou and Yuan Yuan, Profiles of self-shading, sinking phytoplankton with finite depth J. Math. Bio, 2009 Jul;59(1):105-22
  21. T. Kolokolnikov, M.J. Ward and J. Wei, Spot self-replication and dynamics for Schnakenburg model in two dimensional domain J. Nonlinear Science, 2008, 1432-1467
  22. David Iron, T. Kolokolnikov, John Rumsey and Juncheng Wei, Stability of curved interfaces in the perturbed two-dimensional Allen-Cahn system SIAM J. Appl. Math. Volume 69, Issue 5, pp. 1228-1243 (2009)
  23. T. Kolokolnikov and J. Wei, Positive clustered layered solutions for the Gierer-Meinhardt system, JDE 2008, 245(15), 964-993
  24. Mustapha Tlidi, Majid Taki and T. Kolokolnikov, Introduction: Dissipative localized structures in extended systems, CHAOS 17, 037101 ,2007
  25. T. Kolokolnikov and Mustapha Tlidi, Spot deformation and replication in the two-dimensional Belousov-Zhabotinski reaction-diffusion system, Physical Review Letters, Vol.98 2007(18), article 188303.
  26. T. Kolokolnikov, M. Ward and J. Wei, Self-replication of mesa patterns in reaction-diffusion models Physica D, Vol.236(2), 2007, Pages 104-122
  27. T. Kolokolnikov, M. Ward, W. Sun and J. Wei, The Stability of a Stripe for the Gierer-Meinhardt Model and the Effect of Saturation SIAM J. Appl. Dyn. Systems, Vol. 5, No. 2, (2006), pp.~313-363.
  28. K. Kang, T. Kolokolnikov and M.J. Ward, The Stability and Dynamics of a Spike in the One-Dimensional Keller-Segel model , IMA J Appl Math, April 2007; 72: 140 - 162.
  29. T. Kolokolnikov, T. Erneux and J. Wei, Mesa-type patterns in the one-dimensional Brusselator and their stability Physica D 214(2006) 63-77
  30. T. Kolokolnikov, M.J. Ward and J. Wei, Slow Translational Instabilities of Spike Patterns in the One-Dimensional Gray-Scott Model, , Interfaces and Free Boundaries, Vol. 8, No. 2, (2006), pp.~185-222.
  31. T. Kolokolnikov, M.J. Ward and J. Wei, The Existence and Stability of Spike Equilibria in the One-Dimensional Gray-Scott Model: The Low Feed Rate Regime, Studies in Appl. Math., Vol. 115, No. 1, (2005), pp.~21-71.
  32. T. Kolokolnikov, M. J. Ward and Michele Titcombe, Optimizing the Fundamental Neumann Eigenvalue for the Laplacian in a Domain with Small Traps, European Journal of Applied Math, 2005(16), 161-200.
  33. T. Kolokolnikov, M. J. Ward and Juncheng Wei, The Existence and Stability of Spike Equilibria in the One-Dimensional Gray-Scott Model on a Finite-Domain, Applied Math Letters, Vol. 18, No. 8, (2005), pp.~951-956.
  34. T. Kolokolnikov, M. J. Ward and Juncheng Wei Zigzag and Breakup Instabilities of Stripes and Rings in the Two-Dimensional Gray-Scott Model Studies in Appl. Math., Vol. 16, No. 1, (2006), pp.~35-95
  35. T. Kolokolnikov, Thomas Erneux, Michele Nizette, Nicolas Joly and Serge Bielawski, The Q-switching instability in passively mode-locked lasers Physica D 219 (2006) 13-21
  36. T. Kolokolnikov, M. J. Ward and Juncheng Wei, The Existence and Stability of Spike Equilibria in the One-Dimensional Gray-Scott Model: The Pulse-Splitting Regime , Physica D, Vol. 202, No. 3-4, (2005), pp. 258-293.
  37. T. Kolokolnikov and Juncheng Wei, On Ring-Like Solutions for the Gray-Scott Model: Existence, Instability and Self-Replicating Rings , Eur. J. Appl. Math., 16(2005), no.2, 201-237.
  38. T. Kolokolnikov and M. J. Ward, Bifurcation of Spike Equilibria in the Near-Shadow Gierer-Meinhardt Model , Discrete and Continuous Dynamical Systems B, Vol. 4, No. 4, November 2003, 32 pages.
  39. T. Kolokolnikov and M. J. Ward, Reduced Wave Green's Functions and Their Effect on the Dynamics of a Spike for the Gierer-Meinhardt Model, European J. Applied Math, Vol. 14, No. 5, (2003), pp. 513-545.
  40. T. Kolokolnikov and Edgardo S. Cheb-Terrab First-order Ordinary Differential Equations, Symmetries and Linear Transformations , European J. Appl. Math, Vol 14(2), 2003, p. 231-246

Selected conference presentations and talks

  1. Hot spots in crime model, See the video of the talk; or the pdf slides. Presented during PIMS Hot Topics Workshop on Computational Criminology, Sept 2012.
  2. Localized structures, their stability and dynamics in PDEs, Click here for full version including all of the movies (20meg) ; Click here for abbreviated PDF version;
  3. Complex patterns in patricle aggregation models of biological formation CRM/McGill Applied math seminar, Montreal, March 2011
  4. Instability thresholds for a cross-diffusion model and for a crime model , Croucher advanced study institute, Hong Kong, March 2011.
  5. Exact solutions and dynamics for the aggregation model with singular repulsion and long-range attraction , joint AMS-SIAM meeting, New Orelans, January 2011.
  6. Boundary value problems with very sharp structures: numerical challenges , BIRS workshop on geometric and numeric tools for differential equations, Aug 2010.
  7. Ring patterns in patrticle aggregation models , CAIMS meeting, July 2010, St.John's Newfoundland.
  8. A simple PDE model of self-replication in any dimension , CMS Winter meeting, Dec 2009, Windsor, Canada.
  9. Combinatorics and PDEs Abstract: How many solutions does the equation +/-1 +/- 2 +/- 3 +- . . .+/- n = 0 have? In the limit of large n, we derive an asymptotic formula by using the fundamental solution of the heat equation.
  10. Boundary value problems with extremely sharp interfaces , Bluenose numerical analysis days, Dalhousie, June 2008
  11. Ring and smoke-ring solutions in Gierer-Meinhardt model , Second Canada-France Congress, June 2008
  12. Stability of curved interfaces in the perturbed two-dimensional Allen-Cahn system , Applied math Seminar, invited speaker, George Washigton University, 2007.
  13. First Joint CMS/SMM Meeting, Guanajuato, Mexico, 2006, Spot replication in Belouzov-Zhabotinskii reaction.
  14. Invited speaker, Workshop on reaction-diffusion systems, Hong Kong 2006.
  15. Self-replication in reaction-diffusion systems, Limit Problems in Analysis, May 2006, Leiden.
  16. Coarsening and self-replication of mesa patterns in reaction-diffusion systems, Dalhouse colloquium, February 2006
  17. The Q-switching instability in passively mode-locked lasers CLEO 2005, Munich, Germany
  18. Spots, stripes, and labyrinths in reaction diffusion systems, SIAM Dynamical systems 2005, Snowbird, Utah
  19. Mesa-type structures and their stability in the Brusselator , Free boundary problems: theory and applications, June 2005, University of Coimbra, Portugal
  20. Young mathematicians Conference in PDE and Dynamical Systems (Jan 2004). Speaker, Stripe Instabilities in the Two-Dimensional Gray-Scott Model
  21. SIAM Dynamical systems conference, Utah (May 2003). Speaker, Near-shadow Gierer-Meinhardt system: spike bifurcations and spikes near the boundary
  22. BIRS workshop on pattern formation, Alberta (August 2003). Speaker, Coupled regime of the Gray-Scott model: self-replication and oscillatory instabilities
  23. With E.S. Cheb-Terrab and A.D. Roche, 1999, The Search for and Classification of Integrable Abel ODE Classes. Poster for ISSAC 1999

PhD Thesis

Pattern formation in reaction-diffusion models far from the Turing regime, 2004. Supervisor: M.J. Ward.

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