The Differential Equations and Dynamical Systems Group
Contents:
Faculty
- Hermann Brunner
Numerical analysis of Volterra-type integral and integro-differential equations; Computational solution of nonlinear reaction-diffusion problems with memory terms and blow-up solutions. - Andy Foster
Dynamical systems; Mathematical modelling; Applications in ecology, cell population biology, physiology and finance. - Chun-Hua Ou
Applied differential equations (PDEs and ODEs) and dynamical systems; Mathematical biology; Applied analysis methods for differential equations. - Amy Hurford
Mathematical modelling in biology; Applications to epidemiology, evolutionary biology, and ecology; Model parametrization and selection. - Danny Summers
Nonlinear dynamics in the sciences; Modelling; Applications in the physical sciences - Yuan Yuan
Delay differential equations; Dynamical systems; Neural network; Computation of differential equations (symbolic and numerical) - Xiaoqiang Zhao
Asymptotic behavior and special solutions of nonlinear evolution equations; Global dynamics and stability in infinite dimensional dynamical systems; Mathematical models in population biology and epidemiology.
Graduate Students
| Name | Program | Years in Program | Supervisor(s) |
| Carl Howell | M.Sc. (part-time) | 2001- | Foster / Gosine |
| Riu Hu | Ph.D. | 2006- | Yuan |
| Yu Jin | Ph.D. | 2005- | Zhao |
| Brian Johansen | M.Sc. | 2004- | Brunner |
| Yijun Lou | Ph.D. | 2007- | Zhao |
| Cathy McFadyen | M.Sc. (part-time) | 2004- | Foster / Anderson |
| Zakaria Mohamad | M.Sc. | 2006- | Yuan |
| Shannon Sullivan | Ph.D. (part-time) | 2001- | Foster / Grant |
| Michael White | M.Sc. | 2005-2008 | Zhao |
| Wei Yuan | M.Sc. | 2006- | Ou / Yuan |
| Zhaoyu Yin | M.Sc. | 2007- | Brunner |
Recent Graduates
| Name | Program | Supervisor(s) | Thesis Title | Current Status |
| Natasha Kirby | M.Sc. ('06) | Foster | Dynamical systems models of asset pricing | Ph.D., University of Western Ontario |
| Leo Lee | M.Sc. ('06) | Yuan | Stability and bifurcation in systems of tri-neurons with multiple time delays | China |
| Jingtang Ma | Ph.D. ('04) | Brunner | Discontinuous Galerkin methods and cascading multigrid methods for integro-differential equations | Assistant Professor, Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing |
| Jessica Rose | M.Sc. ('06) | Foster / Grant | Dynamical systems analysis of HIV immunopathogenesis and the effects of antiretroviral treatment interruption | Ph.D., Bar-Ilan University, Israel |
| Robin Swain | M.Sc. ('03) | Foster | The Morris-Lecar equations with delay | Ph.D., Imperial College, UK |
| Lin Wang | Ph.D. ('03) | Zou | Dynamics of some neural network models | Assistant professor, Dept. of Math and Statistics, Univ. of New Brunswick, Canada |
| Dashun Xu | Ph.D. ('04) | Zhao | Asymptotic behaviour and traveling waves for some population models | Assistant professor, Dept. of Math, South Illinois University, USA |
| Fang Zhang | Ph.D. ('06) | Zhao | Global dynamics of some spatially heterogeneous population models | Postdoctoral fellow, Univ. of New Brunswick, Canada |
Courses
Undergraduate Courses
- AMAT 3100 Introduction to Dynamical Systems
- AMAT 3161 Ordinary Differential Equations II
- AMPM 3260 Ordinary Differential Equations I
- AMAT 4160 Partial Differential Equations I
- AMAT 4170 Partial Differential Equations II
- AMAT 4190 Mathematical Modelling
Graduate Courses
- MATH 6100 Dynamical Systems
- MATH 6102 Mathematical Biology
- MATH 6104 Infinite Dimensional Dynamical Systems
- MATH 6121 Functional Differential Equations
Journals
There are a lot of journals in differential equations and dynamical systems. Many of the following journals are available, either electronically or in hardcopy format at the Queen Elizabeth II Library.
- Advances in Differential Equations
- Communications in Partial Differential Equations
- Differential and Integral Equations
- Discrete and Continuous Dynamical Systems
- Dynamics of Continuous, Discrete and Impulsive Systems
- Ergodic Theory and Dynamical Systems
- Int. J. Bifurcation and Chaos
- J. Differential Equations
- J. Dynamics and Differential Equations