Demographics of co-aging complex systems: from sickly worms to chess engines

Aging, as defined in terms of the slope of the probability of death versus time (hazard curve), is a generic phenomenon observed in nearly all complex systems. Theoretical models of aging predict hazard curves that monotonically increase in time, in discrepancy with the peculiar ups and downs observed in empirically. Here we introduce the concept of co-aging, where the demographic trajectories of multiple cohorts couple together, and show that co-aging dynamics can account for the anomalous hazard curves exhibited by some species. In our model, multiple interdependency networks inflict damage on one other proportional to their number of functional nodes. We then fit our model predictions to three datasets describing (1) co-aging worm-pathogen populations (2) competing tree species. Lastly, we gather the mortality statistics of (3) machine-against-machine chess games to demonstrate that co-aging dynamics is not exclusive to biological systems

Deterministic and Stochastic Research of Cubic Population Model with Harvesting

A detailed examination of the effect of harvesting on a population has been carried out by extending the standard cubic deterministic model by considering a population under Allee effect with a quadratic function representing harvesting. Weak and strong Allee effect transitions, carrying capacity, and Allee threshold change according to harvesting are first discussed in the deterministic model. A Fokker-Planck equation has been obtained starting from a Langevin equation subject to correlated Gaussian white noise with zero mean, and an Approximate Fokker-Planck Equation has been obtained from a Langevin equation subject to correlated Gaussian colored noise with zero mean. This allowed to calculate the stationary probability distributions of populations, and thus to discuss the effects of linear and nonlinear (Holling type-II) harvesting for populations under Allee effect and subject to white and colored noises, respectively