Analytical Investigation of Pursuit and Evasion Games for Second-Order Parameterized Systems
This paper considers a pursuit-evasion differential game where the dynamics of play-
ers are governed by second-order parameterized differential equations. This model substantially
generalizes the problem formulation by extending the classical inertial motion to oscillating and
exponentially unstable dynamic regimes. A family of parallel pursuit strategies (Π-strategy) for the
pursuer is constructed, and exact necessary and sufficient conditions for guaranteed capture in a
finite time interval are established alongside explicit analytical formulas for optimal capture time.
Furthermore, an explicit evasion strategy for the evader is proposed, lower bounds for the distance
between players are derived, and conditions for guaranteed evasion over an infinite time horizon
are proven. The results obtain generalize and extend classical research on se
1. Isaacs, R. Differential Games. NY: John Wiley and Sons, (1965), 385 p.
2. Pontryagin, L.S. Selected Works. Moscow: MAKS Press, (2004), 551 p. (in Russian)
3. Krasovskii, N.N.; Subbotin, A.I. Game-Theoretical Control Problems. NY: Springer, (2011), 517 p.
4. Petrosjan, L.A. Differential Games of Pursuit. Ser. Optim, vol. 2. Singapore: World Scientific Publ.,
(1993), 340 p. DOI: 10.1142/1670
5. Azamov, A. On the quality problem for simple pursuit games with constraint. Serdica Bulgariacae Math.
Publ., 12 (1986), no. 1, 38–43. (in Russian)
6. Azamov, A.A.; Samatov, B.T. The P-strategy: analogies and applications. In: Proc. The Fourth Int.Conf.
Game Theory and Management (GTM 2010), June 28-30, 2010, St. Petersburg, Russia, 4 (2010), 33–47.
7. Samatov, B.T.; Soyibboev, U.B. Differential game with a lifeline for the inertial movements of players.
Ural Math. J. 7 (2021), no. 2, 94–109. DOI: 10.15826/umj.2021.2.007
8. Mamadaliyev, N. A.; Mustapokulov, Kh. Ya. Construction of P-strategies in a simple pursuit-evasion
game with impulse control. Acta NUUz 2/2.1. (2024), 164–175. (in Russian)
9. Mustapokulov, Kh. Ya. Pursuit-Evasion Problems for Second-Order Differential Games with Impulse
Control. Acta NUUz 2/1.1. (2025), 178–184. (in Russian)
10. Mamadaliyev, N. A.; Mustapokulov, Kh. Ya. A Linear Differential Pursuit Game with Impulse Controls.
Acta NUUz 2/2. (2025), 171–178. (in Russian)
11. Mamadaliyev, N. A.; Mustapokulov, Kh. Ya. Pursuit Problem for Differential-Difference Equations of
Neutral Type. Journal of Mathematical Sciences 277 (2023), no. 3, 438–448. DOI 10.1007/s10958-023-
06846-8
12. Mamadaliyev, N. A.; Mustapokulov, Kh. Ya. On the Invariance of a Constant Multivalued Mapping in a
Heat Conduction Problem with Impulse Control in the Presence of Time Delay. Bulletin of the Institute
of Mathematics 6 (2023), no. 6, 90–98. (in Russian)
Copyright (c) 2026 «ВЕСТНИК НУУз»
Это произведение доступно по лицензии Creative Commons «Attribution-NonCommercial-ShareAlike» («Атрибуция — Некоммерческое использование — На тех же условиях») 4.0 Всемирная.
.jpg)
2.png)
