Director of Bath IMI / Professor of Applied Mathematics

4 West 4.12

Dept of Mathematical Sciences

Email: j.h.p.dawes@bath.ac.uk

# Jonathan Dawes

## Profile

My research falls generally within the field of applied mathematics and is best described as `applied dynamical systems'.

I use a variety of techniques including bifurcation theory and multiple-scale asymptotics to understand the dynamics of an excitingly broad variety of physical and biological systems.

I have worked on problems in symmetric dynamical systems theory, pattern formation, the fluid mechanics of thermal convection, viscous fluid coiling, the stick-slip dynamics of sliding interfaces, mathematical epidemiology and population dynamics.

Recent and current projects include:

- localised states in pattern-forming systems
- dynamics near robust heteroclinic cycles
- instabilities in thin liquid crystal films
- functional responses in predator-prey models
- information spread over networks

I am Director of the Bath Institute for Mathematical Innovation (Bath IMI) which supports mathematical activities across campus and develops collaborative projects between mathematical sciences and other departments, and with external partner organisations.

I am also currently Deputy Director of the Centre for Networks and Collective Behaviour (CNCB).

Further information can be found on my personal home page.

### Publications

Minors, K. and Dawes, J. H.P., 2017. Forthcoming. Invasions Slow Down or Collapse in the Presence of Reactive Boundaries. *Bulletin of Mathematical Biology*

Putelat, T., Dawes, J. H.P. and Champneys, A. R., 2017. A phase-plane analysis of localized frictional waves. *Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences*, 473 (2203), 0606.

Dawes, J. H. P. and Williams, J. L. M., 2016. Localised pattern formation in a model for dryland vegetation. *Journal of Mathematical Biology*, 73 (1), pp. 63-90.

Dawes, J. H. P., 2016. After 1952:the later development of Alan Turing's ideas on the mathematics of pattern formation. *Historia Mathematica*, 43 (1), pp. 49-64.

Morgan, D. and Dawes, J. H. P., 2014. The Swift–Hohenberg equation with a nonlocal nonlinearity. *Physica D: Nonlinear Phenomena*, 270, pp. 60-80.

Dawes, J. H. P. and Susanto, H., 2013. Variational approximation and the use of collective coordinates. *Physical Review E*, 87 (6), 063202.

Dawes, J. H. P. and Souza, M. O., 2013. A derivation of Holling's type I, II and III functional responses in predator-prey systems. *Journal of Theoretical Biology*, 327 (1), pp. 11-22.

Dawes, J. H. P., 2013. Comment on "The effect of rotation on the Rayleigh-Bénard stability threshold" [Phys. Fluids 24, 114101 (2012)]. *Physics of Fluids*, 25 (5), 059101.

Putelat, T., Willis, J. R. and Dawes, J. H. P., 2012. Wave-modulated orbits in rate-and-state friction. *International Journal of Non-Linear Mechanics*, 47 (2), pp. 258-267.

Burke, J. and Dawes, J. H. P., 2012. Localized states in an extended Swift–Hohenberg equation. *SIAM Journal on Applied Dynamical Systems*, 11 (1), pp. 261-284.

Dawes, J.H.P. and Penington, C.J., 2012. Scaling laws for localised states in a nonlocal amplitude equation. *Geophysical and Astrophysical Fluid Dynamics*, 106 (4-5), pp. 372-391.

Dawes, J. H. P. and Giles, W. J., 2011. Turbulent transition in a truncated one-dimensional model for shear flow. *Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences*, 467 (2135), pp. 3066-3087.

Putelat, T., Dawes, J. H. P. and Willis, J. R., 2011. On the microphysical foundations of rate-and-state friction. *Journal of the Mechanics and Physics of Solids*, 59 (5), pp. 1062-1075.

Tsai, T. L. and Dawes, J. H. P., 2011. Dynamics near a periodically forced robust heteroclinic cycle. *Journal of Physics: Conference Series*, 286 (1), 012057.

Taylor, C. and Dawes, J. H. P., 2010. Snaking and isolas of localised states in bistable discrete lattices. *Physics Letters A*, 375 (1), pp. 14-22.

Dawes, J. H. P. and Lilley, S., 2010. Localized states in a model of pattern formation in a vertically vibrated layer. *SIAM Journal on Applied Dynamical Systems*, 9 (1), pp. 238-260.

Postlethwaite, C. M. and Dawes, J. H. P., 2010. Resonance bifurcations from robust homoclinic cycles. *Nonlinearity*, 23 (3), pp. 621-642.

Putelat, T., Dawes, J. H. P. and Willis, J. R., 2010. Regimes of frictional sliding of a spring-block system. *Journal of the Mechanics and Physics of Solids*, 58 (1), pp. 27-53.

Dawes, J. H. P., 2010. The emergence of a coherent structure for coherent structures: localized states in nonlinear systems. *Philosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences*, 368 (1924), pp. 3519-3534.

Dawes, J. H. P., 2009. Modulated and localized states in a finite domain. *SIAM Journal on Applied Dynamical Systems*, 8 (3), pp. 909-930.

Putelat, T., Willis, J. R. and Dawes, J. H. P., 2008. On the seismic cycle seen as a relaxation oscillation. *Philosophical Magazine*, 88 (28), pp. 3219-3243.

Dawes, J. H. P. and Proctor, M. R. E., 2008. Secondary Turing-type instabilities due to strong spatial resonance. *Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences*, 464 (2092), pp. 923-942.

Dawes, J. H. P., 2008. Localized pattern formation with a large-scale mode: slanted snaking. *SIAM Journal on Applied Dynamical Systems*, 7 (1), pp. 186-206.

Morris, S. W., Dawes, J. H. P., Ribe, N. M. and Lister, J. R., 2008. Meandering instability of a viscous thread. *Physical Review E*, 77 (6), 066218.