Dr Natalia Janson

• 2008 – now - Senior Lecturer in Applied Mathematics, Department of Mathematical Sciences, Loughborough University, UK
• 2003 – 2008 - Lecturer in Applied Mathematics, Department of Mathematical Sciences, Loughborough University, UK
• 2000 – 2003 - Research Associate, Physics Department, Lancaster University, Lancaster, UK
• 1997 - PhD in physics and mathematics on the basis of thesis "Reconstruction of dynamical systems from experimental data", Physics Department, Saratov State University, Saratov, Russia

General expertise

Nonlinear dynamical systems, bifurcations theory, oscillations, dynamical chaos, delay differential equations, random processes, data analysis, applications in biology, mathematics of cognition.

Current research focus

Artificial intelligence based on plastic dynamical systems, explainable artificial intelligence, dynamical systems for learning, self-organising vector fields, neural networks.

Past research areas

Synchronization of oscillations, noise-induced phenomena in nonlinear dynamical systems, dynamical systems with delay, nonlinear time series analysis, modelling dynamical systems, global reconstruction of dynamical systems from experimental data, applications in medicine and biology.

Book and Book Chapters 

1. A.G. Balanov, N.B. Janson, D.E. Postnov & O.V. Sosnovtseva (2009) "Synchronization: from simple to complex" Springer. (The book describes general mechanisms for synchronization using analytical calculations supported by numerical simulations and physical and biological experiments)
2.  O.V. Sosnovtseva, D.E. Postnov, N.B. Janson, A.G. Balanov (2011). Synchronization: A Case in Biological Studies. In: Mosekilde, E., Sosnovtseva, O., Rostami-Hodjegan, A. (eds) Biosimulation in Biomedical Research, Health Care and Drug Development, pp. 285-310, Springer, Vienna. 
3. N.B. Janson, A.N. Pavlov, V.S. Anishchenko (2003) Global Reconstruction: Application to Biological Data and Secure Communication, In: G. Gouesbet and S. E. Meunier-Guttin-Cluzel, (eds) Chaos and Its Reconstruction, pp. 287-317, Nova Science.
4. N.B. Janson, A.G. Balanov and E. Schöll (2007) Control of noise-induced dynamics. In: E. Schöll, H.G. Schuster (eds) Handbook of Chaos Control, pp. 221-273, Wiley‐VCH Verlag. 

Sample of Recent Publications

1. N.B. Janson and C.J. Marsden (2017) Dynamical system with plastic self-organized velocity field as an alternative conceptual model of a cognitive system, Scientific Reports, 7, 17007, ISSN: 2045-2322. DOI: 10.1038/s41598-017-16994-y.
2. N. B. Janson and P. E. Kloeden (2021) Robustness of a dynamical systems model with a plastic self-organising vector field to noisy input signals, The European Physical Journal Plus, 136(7), 720, DOI: 10.1140/epjp/s13360-021-01662-y.
3.  N.B. Janson and P.E. Kloeden (2020) Mathematical consistency and long-term behaviour of a dynamical system with a self-organising vector field, Journal of Dynamics and Differential Equations, 34(1), pp.63-78, ISSN: 1040-7294. DOI: 10.1007/s10884-020-09834-7.
4. N.B. Janson and C.J. Marsden (2021) Optimization with delay-induced bifurcations, Chaos, 31(11), 113126, ISSN: 1054-1500. DOI: 10.1063/5.0058087.
5. N.B. Janson and C.J. Marsden (2021) Delay-induced homoclinic bifurcations in modified gradient bistable systems and their relevance to optimization, Chaos: An Interdisciplinary Journal of Nonlinear Science, 31(9), 093120, ISSN: 1054-1500. DOI: 10.1063/5.0035959.
6. N.B. Janson (2012) Nonlinear dynamics of biological systems, Contemporary Physics 53:2, 137-168 (invited review, explains how dynamical systems can help understand biological systems).

Research Supervision

Postdoctoral Researcher

Dr. Andriy Pototskyy (2006-2009) 

PhD Students

1. Adam Essex, principal supervisor (current)
2. Alex Minns, co-supervisor (current)
3. Jonathan Brooks, principal supervisor (current)
4. Dr. Xinhe Liu, thesis title "Implementation of Dynamical Systems with Plastic Self-organising Velocity Fields”, sole supervisor (completed in 2015)
5. Dr. Scott Dickson, thesis title "Stochastic Neural Network Dynamics: Synchronisation and Control", sole supervisor (completed in 2014)
6. Dr. Christopher Marsden, thesis title "Nonlinear Dynamics of Pattern Recognition and Optimization", sole supervisor (completed in 2012)
7. Dr. Sandhya Patidar, thesis title "Noise-induced Cooperative Dynamics and its Control”, sole supervisor (completed in 2009)

Talks and Lecture Courses

Talk "Towards Explainable Artificial Intelligence using Dynamical Systems with Self-organising Vector Fields". Talk at "Neuromorphic technology: a giant leap for AI" in Loughborough University 26-28 March 2024, AI UK Fringe event supported by the Alan Turing Institute. 

TEDx talk: “Can we resolve the mind-body problem with mathematics?”, October 2016

Talk "The mind as the process in time: a mathematical perspective”, Workshop “Time, Disaster and Decision-making”, organised by the Institute of Advanced Studies, Loughborough University, 27 January 2021.

Lectures on dynamical systems and synchronisation (YouTube playlist)

Mini-video “Can the mind be understood mathematically?”

Press Release

Press release 2022: Faster analogue computer could be based on mathematics of complex systems

Memberships

• Fellow of the Institute of Mathematics and its Applications
• Fellow of the Higher Education Academy
• Member of the London Mathematical Society 

Service

• Member of the EPSRC Mathematical Sciences Prioritisation Panels in 2012, 2018, 2021, 2023, 2024

Current courses

• NTA 301 "Mathematics for Problem Solving", semesters 1 and 2
• MAA 901, "Mathematics for Physics", semester 1
• MAC 300 and MAD300 Final Year Projects

Previous Courses

• MAA 155 "Applied Mathematics" (2006/07-2013/14)
• MAB 303 "Mathematics B" (2010/11-2018/19)
• MAP 205 "Physiological Modelling" (2004/05-2010/11)
• MAC272 "Random Processes and Time Series Analysis" (2003/04-2018/19)