This paper considers a pursuit-evasion differential game where the dynamics of play-ers are governed by second-order parameterized differential equations. This model substantiallygeneralizes the problem formulation by extending the classical inertial motion to oscillating andexponentially unstable dynamic regimes. A family of parallel pursuit strategies (Π-strategy) for thepursuer is constructed, and exact necessary and sufficient conditions for guaranteed capture in afinite 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 distancebetween players are derived, and conditions for guaranteed evasion over an infinite time horizonare proven. The results obtain generalize and extend classical research on se
| Mualliflar | Bekniyazov, Asan, Mustapokulov, Khamdam |
|---|---|
| Jurnal | Ўзбекистон Миллий университети хабарлари |
| Nashriyot | Ўзбекистон Миллий университети |
| ISSN | 2181-7324, 3093-8996 |
| Nashr sanasi | 2026-10-07 |
| Jild | 2 |
| Son | 2.3 |
| Betlar | 43-51 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| Indeksga qo‘shilgan | 2026-10-08 |
Differential game, Pursuit problem, Evasion problem, Parameterized dynamics, Par- allel pursuit strategy, Π-strategy, Guaranteed capture time, Oscillatory motion, Unstable system.
| APA | Bekniyazov, Asan, & Mustapokulov, Khamdam (2026). Analytical Investigation of Pursuit and Evasion Games for Second-Order Parameterized Systems. Ўзбекистон Миллий университети хабарлари, 2(2.3), 43-51. https://journals.nuu.uz/index.php/actanuuz/article/view/15245 |
|---|---|
| GOST (OAK) | Bekniyazov, Asan, Mustapokulov, Khamdam Analytical Investigation of Pursuit and Evasion Games for Second-Order Parameterized Systems // Ўзбекистон Миллий университети хабарлари. – 2026. – T. 2, № 2.3. – P. 43-51. |
| MLA | Bekniyazov, Asan, and Mustapokulov, Khamdam. “Analytical Investigation of Pursuit and Evasion Games for Second-Order Parameterized Systems.” Ўзбекистон Миллий университети хабарлари, 2(2.3), 43-51, 2026. https://journals.nuu.uz/index.php/actanuuz/article/view/15245 |
| Chicago | Bekniyazov, Asan, and Mustapokulov, Khamdam. “Analytical Investigation of Pursuit and Evasion Games for Second-Order Parameterized Systems.” Ўзбекистон Миллий университети хабарлари, 2(2.3), 43-51 (2026). https://journals.nuu.uz/index.php/actanuuz/article/view/15245 |
| Harvard | Bekniyazov, Asan, and Mustapokulov, Khamdam (2026) ‘Analytical Investigation of Pursuit and Evasion Games for Second-Order Parameterized Systems’, Ўзбекистон Миллий университети хабарлари, 2(2.3), 43-51. https://journals.nuu.uz/index.php/actanuuz/article/view/15245 |
| BibTeX | @article{bekniyazovasan2026,
title = {Analytical Investigation of Pursuit and Evasion Games for Second-Order Parameterized Systems},
author = {Bekniyazov, Asan and Mustapokulov, Khamdam},
journal = {Ўзбекистон Миллий университети хабарлари},
year = {2026},
volume = {2},
number = {2.3},
pages = {43-51},
url = {https://journals.nuu.uz/index.php/actanuuz/article/view/15245}
} |
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