AA << have used the formalism of dynamical systems theory to explore a highly simplified model for the interaction of a resource-intensive technological species with its host planet. >>
AA << find four distinct classes of trajectories (..)
Sustainability: For these classes, stable equilibria (..) exist which can be approached monotonically. The population rises smoothly to a steady-state value. The planetary environment is monotonically perturbed from its initial value e0 and reaches a new steady state that can support a large population.
Die-off: For these classes, stable equilibria (..) exist which cannot be approached monotonically. The population overshoots the environment's carrying capacity, reaches a peak, and is forced to decline as the environment reaches its new steady state.
Collapse: For these classes, stable equilibria with nonzero population do not exist. In these cases the population experiences a rapid decline after reaching its peak value. It is noteworthy that collapse can occur even though the population has begun leveling off due to the civilization's switching from high-impact to low-impact energy modalities.
Oscillation: In this class, a stable limit cycle exists rather than an equilibrium. The population and the planetary environment cycle between high and low values. >>
Frank A, Carroll-Nellenback Jonathan, et al. The Anthropocene Generalized: Evolution of Exo-Civilizations and Their Planetary Feedback. Astrobiology. 18 (5), May 1, 2018. doi: 10.1089/ast.2017.1671.
https://www.liebertpub.com/doi/10.1089/ast.2017.1671
Alien apocalypse: Can any civilization make it through climate change? University of Rochester. Jun 5, 2018.
https://m.phys.org/news/2018-06-alien-apocalypse-civilization-climate.html
