property of digraphs, called trophic coherence, which may explain the paradox [1]. Trophic coherence is closely related to cycle structure [2] and to the size of a strongly connected component of mutually reachable elements [3] – and hence to the amount and type of feedback. Trophic coherence can be regarded as a measure of overall directedness [4], and is related to non-normality and stability in a wide range of dynamical systems [5, 6].
The PhD candidate will work, along with Dr Johnson and various collaborators, on the mathematical relationships between feedback, stability and trophic coherence in complex systems. There will also be scope to develop new applications of trophic analysis, particularly geared towards investigating data from neuroscience and ecology.
Funding Notes
Funding may be available through a college or EPSRC scholarship in competition with all other PhD applications.
The scholarship will cover tuition fees, training support, and a stipend at standard rates for 3-3.5 years.
Early applications are strongly recommended; there is a deadline for scholarship applications is in January (annually) to be considered in the first scholarship meeting; however, later applications will also be considered.
Strong candidates are encouraged to make an informal inquiry.
Other scholarship and funding opportunities that are available at Birmingham.
Self-Funded Students Worldwide are welcome to apply.
References
(1) Johnson, S.; Domínguez-García, V.; Donetti, L.; Muñoz, M. A. Proc. Natl. Acad. Sci. USA 2014, 111, 17923–17928.
(2) Johnson, S.; Jones, N. S. Proc. Natl. Acad. Sci. USA 2017, 114, 5618–5623.
(3) Rodgers, N.; Tiño, P.; Johnson, S. Proc. Natl. Acad. Sci. USA 2023, 120, e2215752120.
(4) MacKay, R. S.; Johnson, S.; Sansom, B. Royal Society Open Science 2020, 7, 201138.
(5) Johnson, S. Journal of Physics: Complexity 2020, 1, 015003.
(6) Drysdale, C.; Johnson, S. Frontiers in Applied Mathematics and Statistics 2025, 10, 1512865.
