Spatial Complexity of a Predator-Prey Model with Holling-Type Response

Figure 1

(a) 𝐾−𝑑₁ Bifurcation diagram for model (4) with 𝑟=1, 𝑎=0.125, 𝑏=1, 𝑐=0.7, 𝑚=0.625, 𝑞=0.18, and 𝑑₂=0.2. Hopf and Turing bifurcation lines separate the parameter space into three domains. The other parameters in (b)–(d) are 𝑑₁=0.02; the bifurcation parameter 𝐾 equals (b) 2.8>𝐾_𝐻=2.279; (c) 3.499=𝐾_𝑇; (d) 4.0>𝐾_𝑇>𝐾_𝐻. The real parts Re(𝜆) and the imaginary parts Im(𝜆) are shown by solid curves and dashed curves, respectively.

(a)

(b)

(c)

(d)