Effect of seasonally forced noisy environment on aquatic prey-predator model with water level fluctuations.

In this paper, the impact of environmental noise on prey-predator interactions with seasonal fluctuations in water levels has been studied. Both intensity of noise and water level variations together play a significant role in the dynamics of an aquatic prey-predator system. Analytically, we have shown the existence of a positive solution and its uniqueness, the ultimate bound of the system's solutions, and the global attractivity of the solution. Moreover, parametric conditions for which model species either persist (strongly or weakly) in the system or go into extinction are derived and their biological significance is also discussed. The sufficient condition of stochastic permanence is also analyzed. To justify the analytical results, we have performed numerical simulations of both deterministic and stochastic systems and observed some significant dynamics in the considered system.