Dynamics, Instabilities, and Self-Replication of Spots in Two-Space Dimensions

description to be written; pictures and movies

• The Stability and Dynamics of Localized Spot Patterns in the Two-Dimensional Gray-Scott Model
  with W. Chen (SIAM J. Appl. Dyn. Sys., Vol. 10, No. 2, (2011), pp. 582-666.)

• Spot Self-Replication and Dynamics for the Schnakenburg Model in a Two-Dimensional Domain
  with T. Kolokolnikov and J. Wei (J. Nonlinear Science, Vol. 19, No. 1, (2009), pp. 1-56).

• Reduced Wave Green's Functions and their Effect on the Dynamics of a Spike for the Gierer-Meinhardt Model
  with T. Kolokolnikov (European J. Applied Math., Vol. 14, No. 5, (2003), pp. 513-545.)

• The Dynamics and Pinning of a Spike for a Reaction-Diffusion Model
  with D. McInerney et al. (SIAM J. Appl. Math., Vol. 62, No. 4, (2002), pp. 1297-1328.)

• The Stability of Localized Spot Patterns for the Brusselator on the Sphere
  with I. Rozada and S. Ruuth, (SIAM J. Appl. Dyn. Sys., Vol. 13, No. 1, (2014), pp. 564-627).

• Logarithmic Expansions and the Stability of Periodic Patterns of Localized Spots for Reaction-Diffusion Systems in R^2
  with D. Iron, J. Rumsey, and J. Wei, (J. Nonlinear Science, Vol. 24, No. 5, (2014), pp. 857-912).

• On Accurately Estimating Stability Thresholds for Periodic Patterns of Spots for Reaction-Diffusion Systems R^2
  with D. Iron, J. Rumsey, and J. Wei (Europ. J. Appl. Math., Vol. 26, No. 3, (2015), pp. 325-353.)

• The Dynamics of Localized Spot Patterns for Reaction-Diffusion Systems on the Sphere
  with Phillipe Trinh, (Nonlinearity, Vol. 29, No. 3, (2016), pp. 766-806.)

• Localized Spot Patterns on the Sphere for Reaction-Diffusion Systems: Theory and Open Problems
  with Alastair Jamieson-Lane and Philippe Trinh (book chapter in Mathematical and Computational Approaches in Advancing Modern Science and Engineering, J. Belair et. al editors, Springer 2016, pp. 641-651 (Conference Proceedings for CAIMS 2015))

• The Stability and Slow Dynamics of Localized Spot Patterns for the 3-D Schnakenberg Reaction-Diffusion Model
  with Justin Tzou, Shuangquan Xie, Theodore Kolokolnikov (SIAM J. Appl. Dyn. Systems, Vol. 16, No. 1, (2017), pp. 294-336).

• Spot Dynamics in a Reaction-Diffusion Model of Plant Root Hair Initiation
  with Daniele Avitabile and Victor Brena-Medina (SIAM J. Appl. Math., Vol. 78, No. 1, (2018), pp. 291-319.

• The Stability and Slow Dynamics of Spot Patterns in the 2D Brusselator Model: The Effect of Open Systems and Heterogeneities
  with Justin Tzou (Physica D, Vol. 373, (2018), pp. 291-319).

• Spots, Traps, and Patches: Asymptotic Analysis of Localized Solutions to some Linear and Nonlinear Diffusive Systems,
  (Nonlinearity, Vol. 31, No. 8, (2018), R189).

• Anomalous Scaling of Hopf Bifurcation Thresholds for the Stability of Localized Spot Patterns for Reaction-Diffusion Systems in 2-D
  with Justin Tzou and Juncheng Wei (SIAM J. Appl. Dyn. Sys., Vol. 17, No. 1, (2018), pp. 982-1022).

• Refined Stability Thresholds for Localized Spot Patterns for the Brusselator Model in R^2
  with Yifan Chang, Justin Tzou and Juncheng Wei ( Europ. J. Appl. Math., Vol. 30., No. 4, (2019), pp. 791-828.}