System Stability based on Logistic Growth Model

This paper investigates the stability of a system based on the Logistic growth model. On the basis of the traditional Logistic model, this paper introduces factors such as resource constraints, external environmental factors, delay effects, and the multi-stage nature of the system in order to reflect more realistically the dynamic behaviours in complex systems. By constructing an improved Logistic model, the relationship between system stability and resource saturation effect is analysed, and the influence of external environment and feedback mechanism on system stability is explored. Further, this paper verifies the effectiveness of the Logistic model in describing system stability through qualitative and quantitative comparisons with other classical models. The results show that the Logistic model has good applicability in considering resource constraints and stability, and provides theoretical support for understanding the long-term behaviour of complex systems. The research in this paper provides a new perspective on stability analysis in the field of system dynamics and provides a reference for modelling and optimisation of practical problems.