Laboratory Head

Abdulla A’zamov

Laboratory Head

📧 Email: abdulla.azamov@gmail.com

📞 Telefon: +998 97 718 08 42

🕔 Reception days:

🏢 Office number: 215

📍 Address:

Address: 100174, Tashkent city, Almazar district, University street, house 4

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About Laboratory

The history of the "Dynamical Systems and Their Applications" laboratory of the Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan dates back to 1943, when the institute was established. In 1944, the "Theory of Geophysics" department was opened under the leadership of Prof. V.A. Bugayev. Prof. V.A. Djordjio, V.I. Gubin, and other scientists worked there, mainly engaged in the mathematical study of meteorological problems. Later, the department was renamed "Applied Mathematics." During 1986-94, this department was headed by Prof. B.V. Loginov, and during 1994-2005 by Prof. B.B. Rikhsiyev. During this period, the department conducted scientific research on bifurcation theory, optimal control and differential games, and mathematical modeling (Acad. N.Yu. Satimov, Prof. A.A. Azamov, Prof. B.B. Rikhsiyev, Dr. Sci. G. Ibragimov, Dr. Sci. A.Sh. Kuchkarov, and others).

Since 2005, the department has been headed by Prof. (Academician since 2017) A.A. Azamov. In accordance with Resolution No. PQ-4387 of the President of the Republic of Uzbekistan dated July 9, 2019 "On measures to further develop mathematics education and sciences with state support, as well as to fundamentally improve the activities of the V.I. Romanovskiy Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan," the "Dynamical Systems and Their Applications" laboratory was established on the basis of the "Theory of Dynamical Systems" department. Currently, the laboratory has 7 staff positions: 1 principal research fellow, 3 leading research fellows, 2 senior research fellows, 1 junior research fellow, and 1 laboratory assistant. In particular, Acad. A. Azamov, Prof. G. Ibragimov, Dr. Sci. N. Mamadaliyev, PhD A.A. Abduganiyev, PhD M. Bekimov, PhD A. Tilavov, and others conduct scientific activities on the classical theory of dynamical systems, computational dynamics, mathematical modeling of cyclic processes, control in evolutionary systems, and pursuit problems on graphs.

The department collaborates with universities in our republic such as UzMU, TATU, NamDU, AndDU, GulDU, TerDU, as well as with foreign universities and research centers including ICTP (Italy), KAIST (South Korea), INSPEM (Malaysia), N.N. Krasovskiy Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, V.A. Steklov Mathematical Institute of the Russian Academy of Sciences, M.V. Lomonosov Moscow State University, Faculty of Applied Mathematics and Control Processes of St. Petersburg University, Galgotias University (India), Loughborough (United Kingdom), Al Ain University (United Arab Emirates), University of Delaware (USA), G.I. Marchuk Institute of Computational Mathematics of the Russian Academy of Sciences, Al Ain University of the United Arab Emirates, and Universiti Putra Malaysia.

It has been established that the projectivity property may be lost when extending planar polynomial dynamical systems to the Poincaré sphere, and a continuation method that preserves this property has been proposed.

A program has been created to automatically search for periodic trajectories in three-dimensional quadratic dynamical systems.

A discrete numerical observation (DN-observation) method for constructing Poincaré maps for dynamical systems has been developed and applied to 2, 3, 4-dimensional dynamical systems, particularly to I. Prigogine's "Brusselator" example.

Pursuit and evasion differential games consisting of several pursuers with integral constraints and one evader have been studied. Sufficient conditions for the pursuers' capture have been found, and strategies for the pursuers have been developed. A sufficient condition for evasion has been expressed through the convex hull of the evader's initial positions, and an evasion strategy has been constructed.

A differential game of multiple captures involving multiple pursuers and one evader has been studied. In control problems, some control parameters are constrained to certain sets (geometric constraints), while other control parameters are subject to integral constraints. Geometric constraints were imposed on k components of the players' control parameters, and integral constraints on the remaining n − k components. To achieve d captures, we selected pursuers superior to the evader under geometric constraints (without considering other pursuers).

The effectiveness of the Π-strategy in a differential pursuit game with a "lifeline" has been revealed for players moving in straight lines under controls with geometric constraints. The Π-strategy was adopted in the pursuit game, and necessary and sufficient conditions for player P's victory were determined. By defining the support function of a multivalued mapping and applying its properties, we found an exact formula for the reachable set of evader E in the pursuit game.

A differential game involving m pursuers and one evader moving on the edges of an icosahedron has been studied, and points where escape is possible for the evader in the game have been identified.

A high-precision numerical integration algorithm based on Taylor's formula has been developed for solutions of quadratic dynamical systems. The language of terms in Taylor's formula has been constructed, its N. Chomsky grammars have been studied, and its fractal properties have been revealed.

A suboptimal control function has been constructed for the heat exchange equation on a rod.

Pontryagin's first and second pursuit methods for differential inclusions have been developed.

The pursuit-evasion game along the edges of regular polyhedra in arbitrary-dimensional spaces has been solved.

A mathematical model in the form of discrete dynamical systems of the thermodynamic process of heat exchange in a regenerative air heater has been created, and appropriate software has been developed. Topological properties of limit sets of dynamical systems have been studied.

Laboratory director Academician A. Azamov has been awarded the "Excellence in Public Education" badge, the International Bobur Prize (2015), the "Glory of Labor" order (2016), the honorary title "Honored Scientist of the Republic of Uzbekistan" (2023), and the "Pride of Labor" badge (2025). Additionally, the laboratory's principal research fellow G. Ibragimov has been awarded the International "Pythagoras" Prize (2018), Malaysia's gold and silver medals, the "30th Anniversary of Independence of Uzbekistan Commemorative Badge" (2021). Moreover, in 2025 he was included in the Stanford/Elsevier Top 2% scientists list.