• 133 Citations
  • 8 h-Index
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Personal profile


The research is aimed at obtaining quantitative descriptions and critical thresholds of diffusive processes. One area of focus is mean first passage time problems in the presence of small absorbing traps (the narrow capture problem). A particular new direction of work is that in which the small traps are mobile, a scenario that arises in cellular process and predator-prey dynamics. Challenges include not only how to derive the correct PDE for such problems, but how to solve them using asymptotic and/or numerical methods. A critical question is under which condition(s) a mobile trap becomes more effective than a stationary one. The other major area of focus is the stability and dynamics of patterns in reaction-diffusion systems in one, two, and three spatial dimensions, both near and far from the linear regime. Here, asymptotic and numerical continuation techniques are used to construct and characterise steady-state patterns. Through a combination of analytic and numerical methods, critical thresholds are obtained for various types of instabilities. Delayed bifurcations of these instabilities, previously studied only in the context of ODE's near the linear regime, are also analyzed and their qualitative effects studied. The overarching theme is the techniques of analysis used (asymptotic methods, PDE techniques, numerical and continuation methods, Monte Carlo simulations), and that the quantitative results yielded by the analysis often lead to rich qualitative pictures of the underlying phenomena. 

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traps Physics & Astronomy
Reaction-diffusion Model Mathematics
Nonlocal Problems Mathematics
Mean First Passage Time Mathematics
Eigenvalue Problem Mathematics
First Passage Time Mathematics
Trap Mathematics
Turing Mathematics

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Projects 2019 2020

Research Outputs 2009 2019

  • 133 Citations
  • 8 h-Index
  • 21 Article

Refined stability thresholds for localized spot patterns for the Brusselator model in R2

Chang, Y., Tzou, J. C., Ward, M. & Wei, J. C., Aug 2019, In : European Journal of Applied Mathematics. 30, 4, p. 791-828 38 p.

Research output: Contribution to journalArticleResearchpeer-review

Nonlocal Problems
Eigenvalue Problem
Linear Stability
Lattice Points
Stability Theory

Anomalous scaling of Hopf bifurcation thresholds for the stability of localized spot patterns for reaction-diffusion systems in two dimensions

Tzou, J. C., Ward, M. J. & Wei, J. C., 29 Mar 2018, In : SIAM Journal on Applied Dynamical Systems. 17, 1, p. 982–1022 41 p.

Research output: Contribution to journalArticleResearchpeer-review

Anomalous Scaling
Nonlocal Problems
Hopf bifurcation
Reaction-diffusion System
Hopf Bifurcation

Stabilizing a homoclinic stripe

Kolokolnikov, T., Ward, M., Tzou, C. & Wei, J., 15 Nov 2018, In : Philosophical Transactions of the Royal Society A. 376, 2135, p. 1-13 13 p., 20180110.

Research output: Contribution to journalArticleResearchpeer-review


The stability and slow dynamics of spot patterns in the 2D Brusselator model: the effect of open systems and heterogeneities

Tzou, J. & Ward, M., 15 Jun 2018, In : Physica D: Nonlinear Phenomena. 373, p. 13-37 25 p.

Research output: Contribution to journalArticleResearchpeer-review

reaction kinetics

Optimization of first passage times by multiple cooperating mobile traps

Lindsay, A. E., Tzou, J. C. & Kolokolnikov, T., 2017, In : Multiscale Modeling and Simulation. 15, 2, p. 920-947 28 p.

Research output: Contribution to journalArticleResearchpeer-review

First Passage Time
Boundary conditions
absorbing boundary