Dynamical properties of a biological population with a protected area under ecological uncertainty

In this study, stochastic differential equations with Markovian switching are used to describe the growth of some biological populations with protected areas in a random environment, where both white noise and telegraph noise are included in the ecosystem. In addition, the intrinsic growth rate and intra-specific competition coefficient are both considered to be disturbed by ecological uncertainty. We analyze the asymptotical properties of this system, such as weak persistence and extinction. Moreover, we demonstrate the biological significance and provide some real-life examples to support our main conclusions. Our results show that the establishment of a protection zone has important roles in the biological conservation process, but it is not crucial due to the presence of environmental uncertainty. We describe several theoretically strategies, which are expected to enhance the efficiency of protected areas.