Dynamical systems; Bifurcation theory; Symmetry; Mathematical modeling of physical and biological systems; Climate change.

# William Langford

My research has contributed to advancement of the mathematical fields of Dynamical Systems and Bifurcation Theory. I also like to construct mathematical models of real-world systems, and then use mathematical methods to gain better understanding of those systems and to predict their future behaviour. Mathematically, a dynamical system is often expressed as a system of differential equations. Dynamical systems appear in many areas of science. Some examples of areas in which I have constructed dynamical systems that model real phenomena include: the human cardio-respiratory system, coupled mechanical oscillators, Hamiltonian mechanics, pattern formation in annular convection, secure communication, the Taylor-Couette experiment and the Earth’s climate system. In each case, mathematical analysis had led to new insights.

Currently, the main focus of my research is better understanding of climate change. Climate change is perhaps the outstanding scientific problem facing us today. It is of utmost importance to know how our climate will change in the coming decades and centuries. All possible methodologies must be brought to bear on this problem, including dynamical systems and bifurcation theory. My students, coworkers and I have shown that the Earth climate system may undergo bifurcations, which lead to even more dramatic changes in climate than forecast by standard methods.

I am the Founding Director of the Guelph Climate Dynamics Laboratory (GCDL), which is committed to better forecasting of climate change, using dynamical systems methodology. The other Principal Investigators of GCDL are Dr. Allan Willms in this Department and Dr. Greg Lewis of UOIT. The GCDL is a node of the Mathematics and Climate Research Network (MCRN), sponsored by the National Science Foundation of the USA. This gives us access to expertise at other nodes of MCRN and to extra resources for our graduate students. Current Ph.D. student Kolja Kypke also is a member of both GCDL and MCRN. We are actively seeking other graduate students, who may be interested in the mathematics of climate change, to join our GCDL group.

- Dynamical systems
- Bifurcation theory
- Mathematical modelling
- Differential equations
- Pattern formation
- Climate change

**Topological Climate Change and Anthropogenic Forcing**

Kolja Kypke, M.Sc. (2019)

**An Energy Balance Model of Climate Change Incorporating the Roles of Carbon Dioxide and Water Vapour as Greenhouse Gases**

Brady Dortmans, M.Sc. (2017)

**Models of Cytokine Dynamics During Cytokine Storms and Synergy During Virus and Drug Combination Therapy**

Marianne Waito (Wilcox) Ph.D (2016)

**A Model of the Effects of Fluid Variation Due to Body Position on Cheyne-Stokes Respiration**

Marianne Waito (Wilcox) M.Sc. (2013)

**Double Hopf bifurcation with Huygens' symmetry**

Petko Kitanov, Ph.D. (2011)

- Kolja L. Kypke,
**William F. Langford**and Allan R. Willms (2020). Anthropocene Climate Bifurcation. Submitted to*Nonlinear Processes in Geophysics (EGU)*. - Kolja L. Kypke,
**William F. Langford**. (2020). Topological Climate Change.*International Journal of Bifurcation and Chaos*. Accepted to appear in*Vol. 20*. - Brady Dortmans,
**William F. Langford**and Allan R. Willms. (2019). An Energy Balance Model for Paleoclimate Transitions.*Climate of the Past (EGU)*. 15(2): 493-520. - Allan R. Willms, Petko M. Kitanov and
**William F. Langford**. (2017). Huygens' clocks revisited.*Roy. Soc. Open Sci.4: 170777*. - Marianne Wilcox, Allan R. Willms and
**William F. Langford**. (2015). A Model of the Effects of Fluid Variation Due to Body Position on Cheyne-Stokes Respiration.*Bull. Math. Biol.77*: 488-498. - Petko M. Kitanov,
**William F. Langford**and Allan R. Willms. (2013). Double Hopf Bifurcation with Huygens' Symmetry.*SIAM J. Applied Dynamical Systems. 12*: 126-174. **W.F. Langford**and G.M. Lewis. Poleward expansion of Hadley cells.*Canadian Applied Mathematics Quarterly 17 (2009)*105-119.- G.M. Lewis and
**W.F. Langford**(2008). Hysteresis in a rotating differentially heated spherical shell of fluid.*SIAM J. Appl. Dyn. Syst. 7 1421-1444, DOI*: 10.1137/070697306.