Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences


We study a linear evasion differential game of two pursuers and one evader. We impose geometric constraints on the control parameters of players. The control sets of pursuers are unit balls, and that of evader is the ball of radius σ,σ>1. Evasion is said to be possible if the state of the evader doesn't coincide with the state of any pursuer for all time. We construct an evasion strategy for the evader that guarantees the evasion from any initial positions of players. Also, we introduce the concept of approach times. We show that the number of approach times doesn't exceed 3.

First Page


Last Page



1. Azamov A.A., Ibaydullaev T., Ibragimov G.I. Differential game with slow pursuers on the edge graphs of a simplex. International Game Theory Review, Vol. 23, Issue 4, 2199001 (2021).

2. Chernous’ko F.L. A Problem of Evasion of Several Pursuers. Prikladnaia Matematika i Mekhanika, Vol. 40, Issue 1, 14-24 (1976).

3. Chernous’ko F.L., Zak V.L. On differential games of evasion from many pursuers. Journal of Optimization Theory and Applications, Vol. 46, Issue 4, 461-470 (1985).

4. Chikrii A.A., Prokopovich P.V. Simple pursuit of one evader by a group. Cybernetics and System Analysis, Vol. 28 Issue 3, 438-444 (1992).

5. Friedman A. Differential Games. Wiley Interscience. New York, USA, 350 pages (1971).

6. Ibragimov G.I., Massimiliano F., Marks R., Pansera B.A. Linear evasion differential game of one evader and several pursuers with integral constraints. International Journal of Game Theory. Vol. 50, Issue 3, 729-750 (2021).

7. Ibragimov G.I., Massimiliano F., Alias A.I., Salimi M., Nurzeehan I. Pursuit and evasion games for an infinite system of differential equations. Bulletin of the Malaysian Mathematical Sciences Society, Vol. 45, 69-81 (2022).

8. Ibragimov G.I., Salleh Y., Alias A.I., Pansera B.A., Massimiliano F. Evasion from Several Pursuers in the Game with Coordinate-wise Integral Constraints. Dynamic Games and Applications, Vol. 13, Issue 3, 819-842 (2022).

9. Ibragimov G.I. Evasion Differential Game of One Evader and Many Slow Pursuers. Dynamic Games and Applications, (2023).

10. Isaacs R. Differential games. John Wiley and Sons, New York, USA, (1965).

11. Kuchkarov A.Sh., Ibragimov G.I., Khakestari M. On a linear differential game of optimal approach of many pursuers with one evader. Journal of Dynamical and Control Systems, Vol. 19, Issue 1, 1-15 (2013).

12. Kuchkarov A.Sh., Ibragimov G.I., Ferrara M. Simple motion pursuit and evasion differential games with many pursuers on manifolds with Euclidean metric. Discrete Dynamics in Nature and Society, 12-20, (2016).

13. Pontryagin L.S. Izbrannye Trudy; MAKS Press: Moscow, (2004).

14. Pontryagin L.S. Linear differential games. SIAM Journal on Control, Vol. 12, Issue 2, 262–267 (1974).

15. Petrosyan L.A. Differential games of pursuit. World Scientific, Singapore, (1993).

16. Petrov N.N. Matrix Resolving Function in the Nonstationary Linear Group Pursuit Problem Concepting Multiple Capture. International Game Theory Review, Vol. 23, Issue 4, 2150016 (2021).

17. Petrov N.N. Group pursuit problem in a differential game with fractional derivatives, state constraints, and simple matrix. Differential Equations, Vol. 55, Issue 6, 841–848 (2019).

18. Salimi M., Massimiliano F. Differential game of optimal pursuit of one evader by many pursuers. International Journal of Game Theory, Vol. 48, Issue 2, 481-490 (2019).



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.