Global population crisis scenarios predicted by a general nonlinear dynamical model

Abstract

We show that a simple nonlinear differential equation (originally studied in the physics of disordered systems) mathematically describes key regimes of global population growth over the past 12000 years. Different growth regimes since the early Neolithic until the present can be interpreted within a single nonlinear rate-feedback equation in appropriate limits. These include the well-known Malthus (exponential) and Verhulst (logistic) growth laws, as well as von Foerster-type hyperbolic growth as a controlled low-order truncation. While older models may provide valid fits to limited time intervals, their approximate nature prevents them from being predictive over longer periods of time. The proposed framework provides a compact analytical setting to explore future scenarios, including a deliberately conservative, worst-case illustration in which the global population could halve as early as 2064 if carrying-capacity constraints became abruptly active today.