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Table 1 Comparison of the modified hybrid method (5.2) and hybrid method [52] for \(L, S_{1}\in ]0,1[\) and \(a=2.0099\), \(q_{1}=0.0189\), \(q_{2}=1.2994\), \(r=10.5923\), \(E=0.9959\), \(k=1.3997\), \(\beta =98.499\), \(\alpha =2.9999\), \(\delta =0.0384\), \(\rho =10.5842\), \(m_{1}=0.6222\), \(m_{2}=0.4422\), \(h\in (0,1)\)

From: Qualitative analysis of a discrete-time phytoplankton–zooplankton model with Holling type-II response and toxicity

h]0,1[ Controlled interval \(I_{1}\) for (7.3) Controlled interval \(I_{2}\) for (7.4)
0.48889569 0<L<0.99288325491279 \(0< S_{1}<0.97880134847096\)
0.58889569 0<L<0.983282763587931 \(0< S_{1}<0.95068201684448\)
0.68889569 0<L<0.97635403882826 \(0< S_{1}<0.93072628972275\)
0.78889569 0<L<0.97111704728074 \(0< S_{1}<0.91582972183557\)
0.88889569 0<L<0.96701917628990 \(0< S_{1}<0.90428485868004\)
0.98889569 0<L<0.96372500134675 \(0< S_{1}<0.89507489723917\)