Because of the competition among populations in the world, cannibalism is practiced by a wide variety of populations. In most populations where cannibals part resources with their immolation, dependent of a size trait is observed. Using this perspective, a juvenile-adult model is developed under the assumption that adults prey juveniles and adults are bigger in size than juveniles. The model incorporates a Holling type I function that proper the intra-specific predation mount of the crowd at that the juvenile is used up, each adult, as a subordinate of the juvenile density making the model applicable to most population structures as compared to those in literature. Furthermore, the presented sufficient conditions in which the system reaches an equilibrium show the exibility of the model. In particular, we discussed the stability conditions of equilibriums.

In this research, we first prove that the stochastic logistic model (10) has a positive global solution. Subsequently, we introduce the sufficient conditions for the stochastically stability of the general form of stochastic differential equations (SDEs) in terms of equation (1), for zero solution by using the Lyapunov function. This result is verified via several examples in Appendix A. Besides; we prove that the stochastic logistic model, by incorporating the Ornstein-Uhlenbeck process is stable in zero solution. Furthermore, the simulated results are displayed via the 4-stage stochastic Runge-Kutta (SRK4) numerical method.