In this paper we study a ratio-dependent predator-prey model with a free boundary caused by predator-prey interaction over a one dimensional habitat. We study the long time behaviors of the two species and prove a spreading-vanishing dichotomy; namely, as $t$ goes to infinity, both prey and predator successfully spread to the whole space and survive in the new environment, or they spread within a bounded area and eventually die out. The criteria governing spreading and vanishing are obtained.
| Mualliflar | Elmurodov, A. N., Yuldoshev , N. |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2025-11-03 |
| Jild | 69 |
| Son | 4 |
| Betlar | 83-95 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2025-4-9 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2025-4-9 · Maqolaning asl sahifasi
free boundary, a prior bounds, existence and uniqueness, ratio-dependent model, spreading-vanishing dichotomy
| APA | Elmurodov, A. N., & Yuldoshev , N. (2025). A free boundary problem with a Stefan condition for a ratio-dependent predator-prey model. O‘zbekiston matematika jurnali, 69(4), 83-95. https://doi.org/10.29229/uzmj.2025-4-9 |
|---|---|
| GOST (OAK) | Elmurodov, A. N., Yuldoshev , N. A free boundary problem with a Stefan condition for a ratio-dependent predator-prey model // O‘zbekiston matematika jurnali. – 2025. – T. 69, № 4. – P. 83-95. – DOI: 10.29229/uzmj.2025-4-9. |
| MLA | Elmurodov, A. N., and Yuldoshev , N. “A free boundary problem with a Stefan condition for a ratio-dependent predator-prey model.” O‘zbekiston matematika jurnali, 69(4), 83-95, 2025. https://doi.org/10.29229/uzmj.2025-4-9 |
| Chicago | Elmurodov, A. N., and Yuldoshev , N. “A free boundary problem with a Stefan condition for a ratio-dependent predator-prey model.” O‘zbekiston matematika jurnali, 69(4), 83-95 (2025). https://doi.org/10.29229/uzmj.2025-4-9 |
| Harvard | Elmurodov, A. N., and Yuldoshev , N (2025) ‘A free boundary problem with a Stefan condition for a ratio-dependent predator-prey model’, O‘zbekiston matematika jurnali, 69(4), 83-95. https://doi.org/10.29229/uzmj.2025-4-9 |
| BibTeX | @article{elmurodovan2025,
title = {A free boundary problem with a Stefan condition for a ratio-dependent predator-prey model},
author = {Elmurodov, A. N. and Yuldoshev , N.},
journal = {O‘zbekiston matematika jurnali},
year = {2025},
volume = {69},
number = {4},
pages = {83-95},
doi = {10.29229/uzmj.2025-4-9},
url = {https://doi.org/10.29229/uzmj.2025-4-9}
} |
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