Fisher information approach to understand the Gompertz model

Abstract

As a measure of sustainability, Fisher information is employed in the Gompertz growth model. The effect of different oscillatory modulations is examined on the system's evolution and Probability Density Function (PDF). For a sufficiently large frequency of periodic fluctuations occurring in both positive and negative feedbacks, the system maintains its initial conditions. A similar PDF is shown regardless of the initial values when there are periodic fluctuations in positive feedback. By periodic fluctuations in negative feedback, the Gompertz model can lose its self-organization. Finally, despite the fact that the Gompertz and logistic systems evolve differently over time, the results show that they are exceptionally similar in terms of information and sustainability.

Keywords

• dynamical system, sustainability, fisher information, periodic fluctuations, probability density function, equilibrium points.