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. 2024 Nov 26;10(23):e40659. doi: 10.1016/j.heliyon.2024.e40659

Figure 5.

Figure 5

Bifurcation illustrations of the commensurate FO FH-R system (3.8) via predetermined centered factors and the most prevalent value are taken into consideration for various FOs (a-I)χ:χ = 0.07, 0.15, 0.21, 0.35, 0.36, 0.55, 0.67, 0.83, 0.87, 0.90, 0.95 and 1 and ℑ ∈ [0.09356,0.55618]. Lyapunov spectra evolution for the subsequent system parameters: (m) time-dependent MLE for ℑ = 0.13 and χ = 0.67, (n) MLE for ℑ = 0.38 and χ = 0.95, (o-p) MLEs as an expression of ℑ in the domains ℑ = [2.0013,4] and ℑ = [0.45231,5.2001] for χ = 0.99, respectively.