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In this paper, we investigate the influence of anti-predator behavior in prey due to the fear of predators with a Beddington–DeAngelis prey–predator model analytically and numerically. We give the existence and stability of equilibria of the model, and provide the existence of Hopf bifurcation. In addition, we investigate the influence of the fear effect on the population dynamics of the model and find that the fear effect can not only reduce the population density of both predator and prey, but also prevent the occurrence of limit cycle oscillation and increase the stability of the system.

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One-year field campaign was conducted from July 2013 to August 2014 at the site of East China University of Science and Technology (ECUST) in urban Shanghai, and mass concentrations and chemical compositions of PM 2.5 were measured. Gaseous pollutants (SO 2 , NO 2 ) and meteorological parameters (wind speed, wind direction, pressure, temperature and relative humidity) were simultaneously obtained. In this study, PM 2.5 mass balances on haze and non-haze days were reconstructed and the sum of secondary inorganic aerosols (SIA) and organic matter (OM) accounted for over 80%. The fraction of nitrate in SIA was much higher on haze days than that on non-haze days, while the corresponding fraction of ammonium was lower, implying that the variations of the sources and formation processes of SIA on haze days. In theory, sulfate and nitrate might be almost fully neutralized by ammonium. Moreover, the sulfur oxidation ratio (SOR) values were much higher than the nitrogen oxidation ratio (NOR) values, indicating the greater oxidation capacity of SO 2 would occur. On haze days, the high NOR values could be explained by the relatively low temperature, the high NO 2 concentration and the potential dominant gas-phase reaction. As for secondary organic aerosol (SOA), the formation processes were usually associated with nitrate formation. In winter, haze pollution episodes occurred more frequently than those in other seasons, associated with the different features of wind speed, wind direction and 72-h backward trajectory. In addition, one case from 17 November 2013 to 4 January 2014 was selected to investigate the formation mechanism of haze pollution episodes. The key factors that affected the haze formation might be the local stable synoptic conditions including weak surface wind, surface temperature inversion and high relative humidity, the long-range transportations from the Northwest and the large amounts of emissions from local sources.