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oai:figshare.com:article/34017881 2026-09-28T17:56:28Z category_1 category_146 category_915 category_15 category_16 category_873 category_502 category_811 portal_5 item_type_1 month_year_09_2026

<p>Three dimensional view at .</p> Khaleel Ahmad (19500666) Sahib Yar (25132868) Abdul Rahim Khan (25132871) Nida Najeeb (25132874) Adil Jhangeer (9711917) Walid Abdelfattah (21380280) Biophysics Space Science Physical Sciences not elsewhere classified Neuroscience Physiology Chemical Sciences not elsewhere classified Astronomical and Space Sciences not elsewhere classified Mathematical Sciences not elsewhere classified univariate enriched theory strictly stronger requirement period doubling route ordered banach spaces intermediate periodic windows every algebraic step enriched bivariate contractions coupled fixed points coupled fixed point rus contractions (). rus contractions () measured convergence factor long time dynamics enriched bivariate map coupled krasnoselskij iteration uniqueness even though enriched bivariate mappings enriched bivariate ciric div >< p sharp sufficient condition coupled iteration rus operator geometric convergence volterra systems two classes single variable reduction yields product space numerical results methodological contribution fabrizio derivative explicit map enrichment constants earlier formulations direct computation coupling doubles contraction constants condition 2 computed independently bifurcation diagram applied first abstract results 1 stated 1 fails <p>The chaotic attractor of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0358480#pone.0358480.g005" target="_blank">Fig 5</a> in the full phase space.</p> 2026-09-28T17:56:21Z Image Figure 10.1371/journal.pone.0358480.g006 https://figshare.com/articles/figure/_p_Three_dimensional_view_at_p_/34017881 CC BY 4.0