  In this paper, we focus on a spatial Holling-type IV predator-prey model
which contains some important factors, such as diffusion, noise (random
fluctuations) and external periodic forcing. By a brief stability and
bifurcation analysis, we arrive at the Hopf and Turing bifurcation surface and
derive the symbolic conditions for Hopf and Turing bifurcation in the spatial
domain. Based on the stability and bifurcation analysis, we obtain spiral
pattern formation via numerical simulation. Additionally, we study the model
with colored noise and external periodic forcing. From the numerical results,
we know that noise or external periodic forcing can induce instability and
enhance the oscillation of the species, and resonant response. Our results show
that modeling by reaction-diffusion equations is an appropriate tool for
investigating fundamental mechanisms of complex spatiotemporal dynamics.
