Power-Law Memory in Living Species and the Distribution of Lifespans

Humans are systems with memory. In many cases, it is shown that this memory obeys power-law. Unstable systems with power-law memory may for a significant time exist as stable systems. Caputo fractional/fractional difference logistic map is a simple discrete system with power-/asymptotically power-law memory and quadratic nonlinearity. In the area of parameters where the fixed point is unstable the distribution of the times of system’s stable evolution under various types of random perturbations obeys the Gompertz-Makeham law, which is the observed distribution of the lifespans of living species, including humans. The underlying reasons for modeling the evolution of humans by fractional systems are the observed power law in human memory and the viscoelastic nature of organ tissues of living species. We also analyzed available data and found that the power law well fits the shortening of telomeres with time. Models with power-law memory may explain the observed decrease at very large ages of the rate of increase of the force of mortality and they imply limited lifespans.