Spike Dynamics and Stability for Reaction-Diffusion Systems in One-Dimension

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• The Stability of Spike Solutions to the One-Dimensional Gierer-Meinhardt Model
  with D. Iron, J. Wei (Physica D, Vol. 150, (2001) pp. 25-62.)

• Asymmetric Spike Patterns for the One-Dimensional Gierer-Meinhardt Model: Equilibria and Stability
  with J. Wei (European J. Appl. Math., Vol. 13, No. 3, (2002), pp. 283-320.)

• Hopf Bifurcation and Oscillatory Instabilities of Spike Solutions for the One-Dimensional Gierer-Meinhardt Model
  with J. Wei (J. Nonlinear Science, Vol. 13, No. 2, (2003), pp. 209-264.)

• The Existence and Stability of Spike Equilibria in the One-Dimensional Gray-Scott Model: The Low Feed Rate Regime
  with T. Kolokolnikov and J. Wei (Studies in Appl. Math., Vol. 115, No. 1, (2005), pp. 21-71.)

• The Existence and Stability of Spike Equilibria in the One-Dimensional Gray-Scott Model: The Pulse-Splitting Regime
  with T. Kolokolnikov and J. Wei (Physica D, Vol. 202, No. 3-4, (2005), pp. 258-293.)

• Slow Translational Instabilities of Spike Patterns in the One-Dimensional Gray-Scott Model
  with T. Kolokolnikov and J. Wei (Interfaces and Free Boundaries, Vol. 8, No. 2, (2006), pp. 185-222.)

• The Dynamics of Multi-Spike Solutions for the One-Dimensional Gierer-Meinhardt Model
  with D. Iron (SIAM J. Appl. Math., Vol. 62, No. 6, (2002), pp. 1924-1951.)

• Numerical Challenges for Resolving Spike Dynamics for Two Reaction-Diffusion Systems
  with W. Sun, T. Tang, and J. Wei (Studies in Appl. Math., Vol. 111, No. 1, (2003), pp. 41-84.)

• The Slow Dynamics of Two-Spike Solutions for the Gray-Scott and Gierer-Meinhardt Systems: Competition and Oscillatory Instabilities
  with W. Sun and R. Russell (SIAM J. Appl. Dyn. Systems., Vol. 4, No. 4, (2005), pp. 904-953.)

• Oscillatory Instabilities of Multi-Spike Patterns for the One-Dimensional Gray-Scott Model
  with W. Chen (European J. Appl. Math., Vol. 20, No. 2, (2009), pp. 187-214).

• The Dynamics and Stability of Spike-Type Solutions to the Gierer-Meinhardt Model with Subdiffusion
  with Y. Nec (Physica D, Vol. 241, No. 10, (2012), pp. 947-963).

• Slowly Varying Control Parameters, Delayed Bifurcations, and the Stability of Spikes in Reaction-Diffusion Systems
  with J. Tzou and T. Kolokolnikov, (Physica D, Vol. 290, (2015), pp. 24-43).

• The Stability of Localized Spikes for the 1-D Brusselator Reaction-Diffusion Model
  with J. C. Tzou and Y. Nec, (Europ. J. Appl. Math., Vol. 24, No. 4, (2013), pp. 515-564).

• An Explicitly Solvable Nonlocal Eigenvalue Problem and the Stability of a Spike for a Class of Reaction-Diffusion System with Sub-Diffusion
  with Y. Nec, (Mathematical Modeling of Natural Phenomena (special issue on anomalous diffusion), Vol. 8, No. 2, (2013), pp. 55-87).

• The Stability and Slow Dynamics of Two-Spike Patterns for a Class of Reaction Diffusion System
  with Y. Nec, (Mathematical Modeling of Natural Phenomena (special issue on Bifurcation), Vol. 8, No. 5, (2013), pp. 206-232).

• Delayed Reaction-Kinetics and the Stability of Spikes for the Gierer-Meinhardt Model
  with Nabil Fadai and Juncheng Wei (SIAM J. Appl. Math. Vol. 77, No. 2, (2017), pp. 664-696).

• Transition to Blowup in a Reaction-Diffusion Model with Localized Spike Solutions
  with Vivi Rottschafer and Justin Tzou (Europ. J. Appl. Math., Vol. 28, No. 6, (2017), pp. 1015-1055).

• A Time-Delay in the Activator Kinetics Enhances the Stability of a Spike Solution to the Gierer-Meinhardt Model
  with Nabil Fadai and Juncheng Wei (DCDS-B, Vol. 23, No. 4, (2018), pp. 1431-1458.)

• Mathematical Modeling of Plant Root Hair Initiation: Dynamics of Localized Patches
  Victor Brena-Medina, A. Champneys, C. Grierson, M.J. Ward, ( SIAM J. Appl. Dyn. Sys., Vol. 13, No. 1, (2014), pp. 210-248).