Pattern Formation in a Cross-Diffusive Holling-Tanner Model

Figure 2

Bifurcation diagram for model (1.1) with parameters 𝑎=0.8,𝑏=0.1, and 𝐷₂₁=0.8. The Turing bifurcation line is 𝑟_𝑇=(707983156𝐷²₁₂−(7436338235+50000𝐴)𝐷₁₂[phone] − 62500𝐴)/(10⁹(𝐷₁₂+1)(4𝐷²₁₂−𝐷₁₂−5)), where 𝐴=10⁹(14.63−2.336𝐷²₁₂−8.784𝐷₁₂). Hopf bifurcation line is 𝑟_𝐻=0.12572. Turing and Hopf lines intersect at the Turing-Hopf bifurcation point (𝐷₁₂,𝑟)=(−0.00489,0.12572) and separate the parametric space into four domains.