Indicators of collapse in systems undergoing unsustainable growth

Unsustainable growth is typical of systems that rely on a finite pool of non-renewable resources that are tapped until they are depleted. The decrease in resource availability eventually leads these systems to a decline. Here we investigate the dynamics of systems that exhibit unsustainable growth and are prone to a collapse to an alternative ("degraded") state. For these systems the possible imminent occurrence of a collapse is difficult to avert because they keep growing as they approach the transition point. It is therefore important to identify some early warning signs that can be used to predict whether the system is approaching a critical and likely irreversible transition to an undesired and degraded state. This study evaluates whether existing theories of precursors of phase transitions based on the critical slowing down phenomenon are applicable as leading indicators of state shift in unsustainable growth dynamics. It is found that such indicators fail to serve as reliable early warning signs of the system's collapse.