{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T20:13:49Z","timestamp":1776802429454,"version":"3.51.2"},"reference-count":23,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T00:00:00Z","timestamp":1763078400000},"content-version":"vor","delay-in-days":317,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100023674","name":"Deanship of Scientific Research, King Khalid University","doi-asserted-by":"publisher","award":["RGP.2\/339\/46"],"award-info":[{"award-number":["RGP.2\/339\/46"]}],"id":[{"id":"10.13039\/501100023674","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p>We investigate the nonlinear dynamics of a discrete\u2010time predator\u2013prey model governed by a Holling Type\u2010II functional response. Starting from a biologically motivated continuous\u2010time system, we derive its discrete analogue via the explicit Euler method and employ nondimensionalization to reduce the number of parameters. The resulting two\u2010dimensional nonlinear system is analyzed for the existence and local stability of fixed points. Analytical conditions are established for the occurrence of flip (period\u2010doubling) and Neimark\u2013Sacker bifurcations, characterizing the transition from steady states to periodic and quasi\u2010periodic behavior as system parameters vary. Employing center manifold theory and normal form computations, we derive expressions for the first Lyapunov coefficient to determine the direction and stability of bifurcating invariant curves. To suppress chaotic dynamics induced by bifurcations, we implement a hybrid feedback control mechanism and establish sufficient conditions under which the controlled system regains local asymptotic stability. Numerical results, bifurcation diagrams, and phase portraits corroborate the theoretical results. The framework developed herein provides a rigorous foundation for analyzing and stabilizing discrete ecological models with nonlinear interaction terms.<\/jats:p>","DOI":"10.1155\/cplx\/9715552","type":"journal-article","created":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T10:44:14Z","timestamp":1763117054000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Bifurcation Dynamics and Complex Behavior in a Discrete\u2010Time Predator\u2013Prey Model With Cross\u2010Species Interaction Incorporating Holling Type\u2010II Response"],"prefix":"10.1155","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7437-5994","authenticated-orcid":false,"given":"Muhammad","family":"Rafaqat","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0001-4221-052X","authenticated-orcid":false,"given":"Syed Tauseef","family":"Saeed","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6217-3626","authenticated-orcid":false,"given":"Salman","family":"Saleem","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8737-8684","authenticated-orcid":false,"given":"Feyisa Edosa","family":"Merga","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2025,11,14]]},"reference":[{"key":"e_1_2_12_1_2","volume-title":"Elements of Physical Biology","author":"Lotka A. 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