Dichotomous-noise-induced Turing pattern formation in a predator-prey model

Abstract

The predator-prey relationship is always influenced by spatiotemporal fluctuations. Here, we investigate a predator-prey model within a dichotomous noise environment to emphasize the regulation of noise parameters (noise strength and autocorrelation time) and the Allee effect on Turing pattern formation. By employing the Furutzu–Novikov procedure for the noise-induced-diffusion system, we can declare that the dichotomous noise will extend the Turing region depending on its regulatory scheme, and it is more sensitive to autocorrelation time (memory) than noise strength. The strong Allee effect from additive predation amplifies the regulation of noise better than the weak Allee effect by reducing the period of the limit cycle to instability. Moreover, an optimal regulation strategy may control the novel dynamic order and be self-organized while the autocorrelation time would enhance these effects. The numeric results concurring with the theoretical results on pattern formation decipher the mechanism of noise regulation in the predator-prey process from time and space.