Impact of noise in a stochastic coral reefs model

As known, coral reefs have important economic and social value, but they are damaged by various environmental factors worldwide. In this work, a delayed coral reefs system with white noise and L$ \acute{e} $vy jumps are studied. First, we examine the existence problem using Lyapunov analysis methods. Then, from a stochastic analysis technique, we studied the problems for the stochastics persistence and extinction. Furthermore, conditions for stochastic bounded in mean were obtained. Our results indicated that large noise intensity was not conducive to populations. The above results may help us better understand the macroalgae and coral reef dynamics in the fluctuating environments. The most important findings of this article are that we studied a variable coefficient coral reef model under various random disturbances and identified the impact of random perturbation and L$ \acute{e} $vy jump on the dynamic properties of the system. Finally, five numerical simulations are presented to check the obtained results.