The analysis of stability and stabilization in dynamical systems, spanning fields such as physical, biological, and engineering, allows for the exploration of complex phenomena. This includes delving into the intricate dynamics of prey and predator relationships, incorporating Allee effects induced by factors like the cost of predation fear and their subsequent impacts. Additionally, nonlinear dynamics serves as a valuable tool to investigate emergent behaviors within these complex systems, shedding light on the intricate interactions and dynamics that underpin them. This interdisciplinary approach fosters a deeper understanding of the complex relationships and behaviors that manifest in natural and engineered systems, enhancing our ability to predict and manipulate their outcomes.