On the Selection and Meaning of Variable Order Operators for Dynamic Modeling

Figure 3

Plots of 𝑞 and 𝜂 for 𝑝=0.25. (a) 𝑞(Ω,𝜉) versus Ω for 𝜉=0.1,0.5,1,1.5, and 2 (going from light to dark). Note that 𝑞 aysmptotes to 2 as Ω increases. (b) Map of 𝑞(Ω,𝜉) where lower values are represented by darker colors. When Ω=1, 𝑞=0.25 for any value of 𝜉. (c) 𝜂(Ω,𝜉) versus Ω for 𝜉=0.1,0.5,1,1.5, and 2 (going from light to dark). (d) Map of 𝜂(Ω,𝜉). The lowest values of 𝜂 occur near Ω=1 and for small damping ratio.

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(b)

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