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The unique existence of the solution, boundedness, and positivity of the temporal model is derived. Stability analysis of positive steady states is analyzed. Stable and unstable regions for both equilibria are drawn in different parametric spaces. The parametric plots for the different initial conditions are drawn. The diffusive prey\u2013predator model is analyzed for the bifurcation and stability regions. It is observed that the stability regions under the effect of diffusion are increased. To gain the numerical solution of the spatially extended prey\u2013predator model, the operator splitting scheme is derived. The scheme preserves the positivity and other important features of the continuous model. Lastly, a test problem is considered to visualize the accuracy of our scheme. To show the physical behavior of the scheme, 3D and 2D plots are drawn, which clearly show the dynamics of the scheme. Theoretical results are supported by simulations.<\/jats:p>","DOI":"10.1155\/cmm4\/6634314","type":"journal-article","created":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T14:08:58Z","timestamp":1773065338000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Bifurcation and Stability of a Spatiotemporal Prey\u2013Predator Model: A Computational Perspective"],"prefix":"10.1155","volume":"2026","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7224-1271","authenticated-orcid":false,"given":"Muhammad Waqas","family":"Yasin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6118-1472","authenticated-orcid":false,"given":"Ahmad","family":"Shafee","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-4271-6272","authenticated-orcid":false,"given":"Muhammad Zafarullah","family":"Baber","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-5182-2725","authenticated-orcid":false,"given":"Baboucarr","family":"Ceesay","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2026,3,9]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10144-003-0168-2"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2024.115164"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2024.107902"},{"key":"e_1_2_10_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2024.115247"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.11948\/20230212"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.ecolsys.31.1.79"},{"key":"e_1_2_10_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tree.2023.09.012"},{"key":"e_1_2_10_8_2","doi-asserted-by":"publisher","DOI":"10.1142\/S1793524523500109"},{"key":"e_1_2_10_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2024.111370"},{"key":"e_1_2_10_10_2","doi-asserted-by":"publisher","DOI":"10.1002\/num.22689"},{"key":"e_1_2_10_11_2","doi-asserted-by":"publisher","DOI":"10.3390\/math11153378"},{"key":"e_1_2_10_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/0169-5347(91)90148-Q"},{"key":"e_1_2_10_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-5193(89)80211-5"},{"key":"e_1_2_10_14_2","doi-asserted-by":"publisher","DOI":"10.21015\/vtm.v11i1.1512"},{"key":"e_1_2_10_15_2","article-title":"Mathematical Investigations of Diffusive Prey-Predator Dynamical System","author":"Yasin M. 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