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Both strategies seem to be effective in managing bifurcation and chaos inside the system. Finally, the main results are validated by numerical evidence. Parameters of the system are varied to produce time graphs, phase portraits, bifurcation diagrams, and maximum Lyapunov exponent (MLE) graphs. The discrete model displays rich dynamics, as seen in the numerical simulations and graphs, indicating a complex and chaotic system. <\/jats:p>","DOI":"10.1142\/s0218127424501207","type":"journal-article","created":{"date-parts":[[2024,7,31]],"date-time":"2024-07-31T14:53:30Z","timestamp":1722437610000},"source":"Crossref","is-referenced-by-count":13,"title":["Complex Dynamics of a Discretized Predator\u2013Prey System with Prey Refuge Using a Piecewise Constant Argument Method"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4900-0488","authenticated-orcid":false,"given":"Rizwan","family":"Ahmed","sequence":"first","affiliation":[{"name":"Department of Mathematics, Air University Multan Campus, Bahawalpur Road, Multan, Punjab, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0278-1352","authenticated-orcid":false,"given":"Abdul Qadeer","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The University of Azad Jammu and Kashmir, Muzaffarabad 13100, Azad Jammu and Kashmir, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-5648-1989","authenticated-orcid":false,"given":"Muhammad","family":"Amer","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Air University Multan Campus, Bahawalpur Road, Multan, Punjab, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-3575-2434","authenticated-orcid":false,"given":"Aniqa","family":"Faizan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Khawaja Fareed University of Engineering and Information Technology, Abu Dhabi Road, Rahim Yar Khan, Punjab, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3206-1900","authenticated-orcid":false,"given":"Imtiaz","family":"Ahmed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur 10250, Azad Jammu and Kashmir, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2024,7,31]]},"reference":[{"key":"S0218127424501207BIB001","first-page":"61-1","volume":"2022","author":"Ahmed R.","year":"2022","journal-title":"Commun. 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