Coexistence of the Bandcount-Adding and Bandcount-Increment Scenarios

Figure 8

Numerically calculated bandcount diagram in the 2D parameter space for 𝑎=0.2, 𝑏=−2.3⋯−1.1, 𝜇=0.25⋯0.75. Both the period adding (gray lines) and the bandcount-adding (gray areas) scenarios can be seen, separated by the boundary curve 𝜏^env. The white curves inside the white box show the (analytically calculated) interior crisis curves 𝜂^𝑟_ℒℛ4 and 𝜂^ℓ_ℒℛ4, which are the boundaries of the bandcount-adding region 𝑄⁷_ℒℛ4. The other white curves show the interior crises corresponding to the respective labels. The band-merging crisis curve 𝛾_add separates 𝑄^add from 𝑄¹. Note that the region in the upper part is an irregular region inside 𝑄¹. The marked rectangle is shown enlarged in Figure 10.