Proceedings of the International scientific and practical conference ―Science, technology and art in global context‖ (October 14-16, 2025) / Publisher website: www.naukainfo.com. – Warsaw, Poland, 2025. - 72 p.

62 Keywords: Non-autonomous, Stochastic Predator-Prey Model, Beddington- DeAngelis Functional Response, Fear Effect, White Noise, Poisson Noises, Existence and Uniqueness, Global Positive Solution. The study of predator-prey systems is one of the important subjects in population dynamics. The predator-prey model usually described by the system of differential equations ( ) ( )( ( )) ( ( ) ( )) ( ) ( ) ( ) ( ( ) ( )) ( ) where ( ) , ( ) represent the population density of prey and predator respectively at time , is the growth rate of prey, measures the strength of competition among individuals of species , is the death rate of the predator, denotes the conversion coefficient, ( ) is the functional response of the predator. In [1] and [2] authors proposed the Beddington – DeAngelis functional response of the form ( ) ( ) In recent years, many experts have begun to study the predator-prey model with the fear effect. So the deterministic predator-prey model with fear effect and the Beddington–DeAngelis functional response has a form ( ) ( ) ( ( ) ( ) ( ) ( ) ( ) ) ( ) ( ) ( ( ) ( ) ( ) ) where fear factor presents the level of fear induced by predators . It is known that environmental noise is an important component in an ecosystem. Therefore, it is reasonable to introduce the white noise term into the corresponding deterministic model. Population systems may suffer abrupt environmental perturbations, such as epidemics, fires, earthquakes, etc. It is natural to introduce centered and non-centered Poisson noises into the population model for describing such discontinuous systems. So, we take into account not only ―small‖