A spatial version of the predator–prey model with Holling III functional response, which includes some important factors such as external periodic forces, noise, and diffusion processes is investigated. For the model only with diffusion, it exhibits spiral waves in the two-dimensional space. However, combined with noise, it has the feature of chaotic patterns. Moreover, the oscillations become more obvious when the noise intensity is increased. Furthermore, the spatially extended system with external periodic forces and noise exhibits a resonant pattern and frequency-locking phenomena. These results may help us to understand the effects arising from the undeniable susceptibility to random fluctuations in the real ecosystems.