Mathematicians from Nizhny Novgorod and Shanghai Study System Stability

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Mathematicians at HSE University–Nizhny Novgorod, in collaboration with colleagues from Tongji University in Shanghai, are investigating the fundamental causes of structural stability in systems and the mechanisms underlying its disruption. In this interview with the HSE News Service, Prof. Olga Pochinka, Head of the International Laboratory of Dynamical Systems and Applications at HSE University–Nizhny Novgorod and leader of the project ‘Qualitative Theory of Systems of Ordinary and Partial Differential Equations,’ discusses the project, which is being implemented as part of HSE University's International Academic Cooperation programme.

The project team is studying systems of differential equations that model processes which remain stable under changes in parameters such as temperature or pressure. This collaboration enables Russian researchers to maintain an active exchange of expertise with the international scientific community.

Olga Pochinka

— How long has the project been underway?

— Our partnership began in 2024, when the laboratory, together with the School of Mathematical Sciences at Tongji University, won HSE University's International Academic Cooperation competition for joint basic research projects. The project is now in its third year of successful implementation.

— Why did you choose this particular partner?  

— Our colleagues in China also specialise in dynamical systems with an emphasis on topology. We have a long-standing collaboration with the project leader on the Chinese side, Prof. Bin Yu, whom we first met in France in 2011. Since then, we have maintained regular contact: he has visited HSE University–Nizhny Novgorod several times, and our team frequently travels to Shanghai. This long-term collaboration has already resulted in a number of joint scientific publications.

— What are the key areas of your work?

— The key area of our work is the study of dynamical systems. In particular, we are extending the class of systems for which the existence of an energy function is already considered resolved. We also plan to obtain fundamental results in the classification of hyperbolic systems and their attractors. Another important objective is to describe how the non-wandering set of a system relates to the topology of the manifold on which it is defined.

— Is it primarily basic or applied research?

— Our focus is on basic research and on developing a theoretical framework that may serve as a foundation for applied research in the future. Many patterns in dynamical systems remain hidden, and a number of them have yet to be uncovered. We plan to continue in this direction and to obtain new results. Although such research does not immediately translate into specific practical applications, its potential for science and technology is enormous.

— So applied research is also expected?

— We work with both ordinary and partial differential equations. The latter are critically important in hydrodynamics, as they make it possible to model extreme natural phenomena such as tsunamis and rogue waves. Under the guidance of Prof. Efim Pelinovsky, our colleagues study the life cycle of a wave—from its formation and development to the conditions under which it is sustained and the factors that lead to its decay.

— What project outcomes would you highlight in particular?

— I would highlight our publication record: we have fully met our publishing commitments. To date, four papers have been published, three of them in A-list journals, and two have been co-authored with our Chinese colleagues.

It is also important to highlight our support for early-career researchers: regular visits by our undergraduate, master’s, and doctoral students to China have been an essential part of the project. Direct interaction with international colleagues helps students stay attuned to global scientific trends, exchange ideas, and conduct truly effective research.